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Book News Annotation:
This introduction to topology employs a methodology somewhat different from other texts. Metric space and point-set topology material are treated in the first two chapters, and algebraic topological material is covered in the remaining two chapters, leading the reader through nontrivial applications of metric space topology to analysis. Treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning and presents relatively little algebraic formalism; at the same time, this treatment provides proofs of some highly nontrivial results. Assumes familiarity with real numbers and some basic set theory. Includes chapter exercises. The authors are affiliated with UCLA. This is an unabridged republication of a work published by Saunders College Publishing, Philadelphia, 1983. This edition contains solutions to selected exercises
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This utility uses the free Flash player plug-in resident in most browsers to allow the user to graph a surface of the form z = f(x,y) on a customized scale and dynamically rotate the three-dimensional picture.
In this applet, a user fills in a grid to create a distribution of numbers. The applet displays the size of the standard deviation and the position of the mean in the distribution. An activity is provided to facilitate the use of the applet to investigate standard deviation.
This suite of five interactive applets (written with GeoGebra) allows exploration of definitions and theorems commonly presented in first-year analysis courses. Topics include sequence convergence, continuity at a point, the Mean Value theorem, Taylor series, and Riemann sums. Included with each applet is a pair of activities: one for becoming comfortable using the applet, and one for using the applet to explore the associated topic in depth.
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Mathematics
Do you know what our graduates say was the most important thing they learned in their math courses? How to communicate their ideas. The experience they got writing lab reports and working in small group situations set them apart from their competition and gave them an advantage in finding jobs after graduation. At Marietta, we'll teach you the practical and the analytical aspects of mathematics, but we also stress the personal and the communicative aspects that surround math in order to prepare you for a career.
As a math major at Marietta, you'll have access to the best technological resources. You'll learn to use graphing calculators and advanced mathematical software that does the number crunching and algebraic manipulations, leaving you more time to understand the ideas and the theory behind the numbers.
All mathematics majors work one-on-one with a faculty member on a senior capstone project. Some projects are expository in nature, while others deal involve partial solutions to open problems. Students write up their findings in a formal paper, and present their results to the faculty and other students. Students whose projects are exceptionally good are encouraged to present their results at regional and national mathematics conferences and/or submit their papers for publication.
You'll have the opportunity to participate in research, independent study, and special honors projects with a faculty mentor. As a senior, you'll carry out your own research project as part of senior capstone experience. Our majors regularly present these projects at regional and national conventions.
Clubs & Organizations
The Marietta College chapter of Kappa Mu Epsilon, the national honorary mathematics society, co-sponsors visiting speakers and offers free tutoring to mathematics students who need help at the introductory levels.
The Louise Clark Bethel Mathematics and Science Scholarship provides tuition, fees, and books for seniors at Marietta High School who rank high in mathematics and science and who otherwise would be unable to attend Marietta College.
The Lewis and Marie Ryan Scholarship benefits deserving Marietta College students majoring in mathematics or science and whose academic standing is in the upper ten percent of the class, and who, without financial assistance, might be unable to attend Marietta College.
The Theodore Bennett Memorial Prize is awarded to the junior considered by the Department of Mathematics to be the most outstanding.
The Leon A. Ruby Scholarship is awarded to deserving students in mathematics who have completed a full year at Marietta
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How to Succeed in Physics by Really Trying
Preparation for this Course
If you had high school physics, you will probably learn the concepts of
this course faster than those who have not because you will be familiar with the language
of physics. Also helpful will be the state of your mathematics preparation – if your
mathematics ability is better than most, you will pick up the mathematical aspects of
physics faster. If you find that your math skills are poor, do not hesitate to seek help
from The Learning Centre in the
Student Services annex as soon as possible.
Learning to Learn
Each of us has a preferred learning style and a preferred means of
learning. Understanding your own style will help you focus on aspects of physics that may
give you difficulty and to use those components of the course that will help you overcome
the difficulty. Obviously, you will want to spend more time on those aspects that give you
the most trouble. If you learn best by hearing, lectures will be very important. If you
learn by explaining, then working with other students will be useful to you. If solving
problems is difficult for you, spend more time learning how to solve problems. In
addition, it is important to understand and develop good study habits. Perhaps the most
important thing you can do for yourself is to set aside adequate, regularly scheduled,
study time in a distraction-free environment.
Answer the following questions for yourself:
Am I able to use fundamental mathematical concepts from algebra, geometry and
trigonometry? (If not, plan a program of review. The Learning Centre schedules seminars on
these topics early in the semester.)
In similar courses, what activity has given me the most trouble? (Spend more time on
this area.) What has been the easiest for me? (Do this first; it will help to build you
confidence.)
Do I understand the material better if I read the book before or after the lecture? (You
may learn best by skimming the material, going to lecture, then undertaking an in-depth
reading.)
Do I spend adequate time studying physics? (A rule of thumb for a class like this is to
devote, on average, 2.5 to 3 hours out of class for each hour in class. For a course
meeting 3 hours each week, that means spending 7 to 10 hours per week studying physics.)
Do I study physics every day? (Spread that 10 hours out over the whole week!) At what
time of the day am I at my best for studying physics? (Pick a specific time and make it a
habit.)
Do I work in a quiet place where I can maintain my focus? (Distractions will break your
routine and cause you to miss important points.)
Working with Others
Scientists or engineers seldom work in isolation from one another, but
rather work co-operatively. You will learn more physics and have more fun doing it if you
work with other students. You may wish to form your own study group with members of your
class. Use email to keep in touch with each other and ask question about the day's
lecture or the upcoming assignments. Your study group is an excellent resource when
reviewing for a test or exam.
Lectures and Taking Notes
An important component of any university course is the lecture. In
physics, this is especially important because your professor will frequently do
demonstrations of physical principles and work example problems on the board. These are
learning activities that will help you to understand the basic principles of physics. Don't
miss lectures, but if you do, ask a friend or member of your study group to provide
you with notes and let you know what happened.
Take your class notes in outline form and fill in the details later. It
can be very difficult to take word for word notes, so just write down the key ideas.
Diagrams should be sketched quickly, with the details added later. After class, edit your
notes, filling in any gaps or omissions and noting things you need to study further. Refer
to the textbook by page, equation number or section number.
Make sure you ask questions in class or see your professor during
office hours (office hours will be listed in the Course Outline handed out at the
beginning of the semester, and posted on his office door). Remember that the only
"dumb" question is one that is not asked.
There may also be an SI (Supplemental Instruction) leader for your
course – if so, watch for the posted meeting time. At the SI meeting the leader (who
is an upper year student who did well in the course) will answer questions and try to
clarify problem areas. If you prefer one on one instruction, Peer tutors are also
available through The Learning Centre; check
their schedule for times.
Using Your Textbook
You've paid a lot of money for that textbook – so don't
just carry it around – use it! All modern textbooks have been designed
to be as interesting as possible and with many kinds of learning aids incorporated in
them. In addition to reading the assigned sections of the text, be sure to work through
all the examples, filling in any missing steps and making note of things you don't
understand. At the end of each chapter there is usually a series of non-mathematical
exercises designed to test your understanding of the concepts covered in the chapter - try
these regularly. Get help right away with the concepts that confuse you!
Tests and Examinations
Taking an examination or test is stressful, but if you feel adequately
prepared and are well rested, your stress will be lessened. Preparing for a test is a
continual process; it begins the moment the last test is completed. You should immediately
go over the test and understand any mistakes you made. If you worked a problem and made
substantial errors, try this: take a piece of paper and divide it down the middle with a
line from top to bottom. In one column, write the proper solution to the problem. In the
other column, write what you did and why. Also write why your solution was incorrect, if
you know. If you are uncertain as to why you made your mistake and how to avoid it again,
talk to your professor. Physics continually builds on fundamental ideas and it is
important to correct any misunderstandings immediately. Warning: While cramming at
the last minute may get you through the present test, you will not adequately
retain the concepts for use on the next test.
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Find a North Miami, FL SAT MathBuilding blocks is what Algebra is about. If the student does not have the fundamentals of Algebra, this is the moment to reinforce concepts before moving on with Algebra 2 syllabus. Important concepts such as quadratic functions and its applications in real world problems are covered in Algebra 2.
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Part 2 targets 2-star and 3-star coaches with the aim of further enhancing ... in this
manual will be useful to coaches and will help them to become a better coach.Mathematics learning difficulties: an analysis of primary teachers' perceptions . ..... The themes were also used to structure the programme, as shown in Table 1: .... research, its development from the early eighties until now, and its influence on ...
Source:
Engineering Mathematics 5th Edition covers a wide range of syllabus requirements. In particular, the book is most suitable for the latest National Certificate and.
Source:
Introduction to Excel Part Two: Formatting an Existing. Spreadsheet. Purpose.
Upon completion of this tutorial you will have learned how to format the following:
.
Source:
Edexcel AS/A level Mathematics Formulae List – Issue 1- September 2009. 3. The formulae in this booklet have been arranged according to the unit in which ...
Source:
Mathematical Methods for Physics and Engineering. The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the ...
Source:
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An Introduction to Tensors for Students of Physics and Engineering
An Introduction to Tensors for Students of Physics and Engineering by Joseph C. Kolecki
Publisher: Glenn Research Center 2002 Number of pages: 29
Description: The book is intended to serve as a bridge from the point where most undergraduate students 'leave off' in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and similar higher-order vector products.
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Polynomial Vocabulary - Definition of a Polynomial Before adding and subtracting polynomials or multiplying polynomials, it is important to know the definition of a polynomial and polynomial vocabulary. This video describes important polynomial definitions and terms including monomial, the degree of a monomial, polynomial degree and standard form. (7:15) Author(s): No creator set
Market Comparison A comparison of the two markets, perfect competition and monopoly, considering the similarities and differences Author(s): No creator set
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Solving Multi-Step Equations It can be difficult to understand solving multi step equations, but after learning how to solve one-step and two-step equations this is the final step in learning how to solve for a variable. Solving multi-step equations is an important skill that involves using additive and multiplicative inverses and the variable that makes the equation true. (00:35) Author(s): No creator set
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Description
A survey course designed to deepen the student's knowledge of the vast literature of mathematics. Historically influential concepts will be examined for their effects on mathematics and the culture in which they evolved. Philosophical and psychological comparisons will be made between the mathematical and scientific developments in Ancient Greek times, in the Renaissance and Newtonian times, and in the 19th and 20th centuries.
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Modeling Population Growth
Differential equations allow us to mathematically model quantities
that change continuously in time. One of the simplest examples of a
changing quantity is the number of plants or animals of a particular
species. Although populations are discrete quantities (that is, they
change by integer amounts), it is often useful for ecologists
to model populations by a continuous function of time. Modeling can
predict that a species is headed for extinction, and can
indicate how the population will respond to intervention.
Populations grow according to the number of individuals that are
capable of reproduction. At the same time, their growth is limited
according to scarcity of land or food, or the presence of external
forces such as predators. In this module, we examine simple
differential equations that model populations. We also introduce and
explore powerful techniques for the geometric analysis of
differential equations: phase space, equilibria, and stability.
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Students are introduced to concepts that will become the foundation for success in other classes. Success in algebra helps prepare the student for a variety of careers in medicine, engineering, technology, business and more. Algebra introduces abstract concepts to students who may already be anxious about their math abilities
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56Introductory Algebra is typically a 1-semester course that provides a solid foundation in algebraic skills and reasoning for students who have little or no previous experience with the topic. The goal is to effectively prepare students to transition into Intermediate Algebra.
Editorial Reviews
About the Author
Elayn Martin-Gay, University of New Orleans
An award-winning instructor and best-selling author, Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also originated the Chapter Test Prep Video CDs to help students during their most "teachable moment" ---as they prepare for a test.
Elayn's experience has made her aware of how busy instructors are and what a difference quality supports make. For this reason, she created the Instructor-to-Instructor video series. These videos provide instructors with suggestions for presenting specific math topic and concepts in basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the CDs useful for review. They are a great resource for suggestions regarding areas they may wish to emphasize, or common trouble areas students experience, that instructors my wish to highlight.
With her textbooks series, the Chapter Test Prep Video Cd, and CD Lecture series, Elayn has sought to put success within the reach of every student and instructor.
Most Helpful Customer Reviews
I am 43 years old and needed to take algebra to finish my AS degree. I have not taken an algebra class in 30 years. This book was the required textbook for my class.
I found this book very organized. In fact it was so organized I rarely needed to take notes on all the rules of algebra. This book helped me to review at the end of each section with the needed sample problems and reviews. It even had up-to-date pictures with algebraic problems that solved real life practical problems.
I highly recommend this book to anyone that needs to understand the basics of algebra.
The product was adequate for my classes. The only drawback when having a different college oriented same product was that cd's were not added to this particular book and I find them very helpful in my learing. Other than that the product was what I wanted. Thank you,.
This book has helped me break down Algebra to a basic form for my son. He has a learning disability and he gets it it may take practice but having the foundation of the problems the way they are presented is very helpful as well as the self test.
The book is in great condition... however I was unaware that it was the "Annotated Instructor's Edition". I did not enjoy opening the package to find this out. Letting people know exactly what they are buying would be a good thing.
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Learning precalculus is easier with the visual emphasis in PRECALCULUS: WITH UNIT-CIRCLE TRIGONOMETRY, Fourth Edition and its accompanying technology tools. This textbook uses a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. David Cohen is known for his clear writing style, as well as the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are introduced much earlier and receive greater emphasis. Many sections contain more examples and exercises involving applications and real-life data. The accompanying CD-ROM and online tutorials give you the practice you need to improve your34.49
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How We Get Our Students to Read the Text Before Class
(MAAOL Version)
Abstract: We describe an email-based approach to reading assignments
that has been very effective in getting our students to read the text
before class. The dramatic impact this approach has had on
our courses is explained through sample assignments and student
responses. We also share the results of seven semesters of student
evaluations and address some implications of using these assignments.
1. Introduction
When students read the text before class, the fundamental nature of
class meetings is changed. The students arrive familiar with basic
concepts and definitions, providing more class time to address the
major ideas and subtleties of the mathematics. In addition, the
instructor is no longer viewed as the sole source of content for the
course, and this encourages greater independence, and more lively
interactions, among students. The challenge, of course, is getting
students to consistently read the text before class for the entire
semester.
Unfortunately, few of our students have experience reading a math text, and
most treat the book as a reference to use after the professor has
presented new material. To counter these habits, one approach is to simply
give a reading assignment for each class meeting. In our experience, most
students are unlikely to read consistently for the entire semester unless
there is some form of direct evaluation to keep them accountable. Since
any assessment during class interferes with the main goal of freeing class
time to discuss mathematics, it is important that such a method use
alternate means to promote the activity of reading. In this article, we
describe how email-based reading assignments have transformed a broad range
of our courses, including Introductory Statistics, Single and Multivariable
Calculus, Linear Algebra, and Geometry.
2. Our Goals, both Big and Small
One of the challenges to learning mathematics is that understanding is
often built in stages, and one's perspective deepens upon revisiting
concepts a second, third, nth time. If class time may be spent
on students' second exposure to basic terminology and elementary
examples, then the class is able to get to deeper mathematics more quickly
and in more detail. Indeed, this moves a class session from simply
introductory lectures to a time when elementary ideas are clarified (as
necessary) and expanded upon.
In addition, we strive in our courses to promote students' logical
reasoning and writing skills. It is often a shock to first year
mathematics students that the instructor would expect them to write (and in
complete sentences!) about mathematical ideas. While one can encourage
such activity on homework and exams, it is ideal to have as many different
activities as possible in which to develop writing skills. By reading a
mathematics textbook for content, as well as through responding to
questions about the reading, we aim to raise the level of students'
writing, along with improving their reading skills.
While these goals are broad and perhaps ambitious, our desires for
individuals on a day-to-day basis are quite modest. We want the students to
be familiar with past and upcoming terminology and to have a rough idea of
the basic concepts from each section. If each student spends some
time reading and preparing for class, then we believe that many of the
bigger goals will be accomplished. Finally, we also desire to reward our
students for their effort, while making sure that the approach to reading
is perceived as reasonable by both student and instructor.
3. The Details of the Assignments
We place the reading assignments on a course webpage, usually in month or
week long segments. This frees class time from announcing or distributing
the assignments and makes the assignments conveniently available to
students outside of class. The posting lists the specific section(s) to
read, which parts should be emphasized, and which can be skipped, if
any. There are also several basic questions that the student should be able
to answer after completing the reading. The questions serve to focus the
students' reading and give them feedback on their level of comprehension;
students email their responses to the instructor before the following class
meeting. This gives the instructor feedback on the level of the students'
understanding before class and allows the instructor to make
adjustments as necessary.
As an example, the following is an assignment
from Calculus II; the course text was [1].
For February 17
Section 3.8 Inverse Trigonometric Functions and Their Derivatives
To read: All, but you can skip the section on
Inverse Trigonometric Functions and the Unit Circle
Reading Questions:
What is the domain of the function arccos(x)? Why?
Why are we studying the inverse trig functions now?
Find one antiderivative of 1/(1+x^2).
We have found that a binary grading scheme works well for the assignments:
a student earns a 1 for sincerely attempting to answer the questions
(independent of whether the answers are correct), or receives a 0 if no
such attempt is made. In addition, the assignments count for 5% of a
student's final grade in the course. This assessment method has several
advantages. First, it emphasizes that a major point of the assignments is
making an honest effort, and also reduces the stress that many students
feel toward assignments in general. Further, this scheme makes the
assessment of the assignments fairly easy for the instructor. For a class
with 30 students, it takes approximately 20 minutes to read and record a
given day's responses from the class. Another effective tactic has been to
require the students to enter a specific subject line in their email
messages. The instructor can then use an email filter to move messages
with that subject line into a specific folder and generate an automatic
response, letting the student know that the assignment has been received.
The student responses are always informative, and they often provide an
excellent starting point for class discussion. We choose several of the
best responses to each assignment and place them on a temporary webpage.
By displaying these responses at the beginning of class, students can
compare their own thoughts on the reading, as well as see the work of some
peers. This activity sparks both questions and responses, often resulting
in discussion of key subtleties in the material. By archiving these web
pages, students are also able to view the responses after class at any
point later in the term.
4. Sample Reading Questions and Student Responses
4.1 From Calculus II
In our calculus sequence, we do not cover inverse trigonometric functions
until Calculus II. The sample assignment in
Section 3 came after we had discussed numeric integration but before we had
covered any techniques of antidifferentiation.
The student responses that were displayed during class were:
The domain of the arccos(x) is [-1,1], because the range of the
cos (its inverse), is [-1,1]. A.V., First-Year
We are studying inverse trig. functions now because by knowing
the derivatives of these functions, we will be able to calculate more
definite integrals using the FTC (Fundamental Theorem of Calculus).
A.C., Sophomore
One antiderivative of 1/(1+x^2) is arctan(x) + 3.
M.K., First-Year
These answers all show that the students understand the fundamental issues
raised by the questions. A.V.'s response shows an understanding of the
relationship between the range of a function and the domain of its
inverse. A.C. gives a nice justification for why we are introducing
the inverse trigonometric functions at this point in the course, and
M.K. demonstrates the important point that the antiderivative is not
unique.
Obviously, not all students gave such precise answers to all questions. In
fact, M.K. completely missed the motivation for studying the inverse
trigonometric functions. However, most students' misunderstandings were
minor and were cleared up at the beginning of the class. This allowed
enough time in a 50 minute class to derive the derivatives of arcsin(x) and
arctan(x) and to give the students 15 minutes of in-class work. Without
knowing the students' level of understanding before class, it is highly
unlikely that we could have accomplished as much in one class meeting. With
no assessed reading assignment, more time would have been spent on
introductory material and motivation. Assessing the reading in class would
not only eat into class time but would also make it more difficult to
adjust the class meeting based on the students' responses.
4.2 From Geometry
The following assignment from early in the semester centered on the
introductory section to the study of Euclidean motions of the plane. While
the material had a new geometric perspective to students, they should have
been familiar with many of the basic ideas from prior courses. The course
text was [3].
For Monday, January 24
Reading Assignment: Section 2.1 (all)
Reading Questions:
What is the difference between a mapping and a function?
Is every mapping a transformation? (Explain, including a
description of a transformation.)
Does every transformation have an inverse? Why or why not?
The following were among the student responses shared in class:
Mapping means that every element a of A has a unique element
b of B that is paired with a. A function is a set of ordered pairs
(a,b) with no two different pairs having the same first element.
Therefore, they have similar definitions. The main difference is
that Mapping is the term used in geometry, rather than the term
Function. M.M., Junior
No every mapping is not a transformation. A transformation
is when the (x,y) are altered or reversed in some way. It consists
of one-to-one and onto functions. When you reverse the pairs, it
does not always result in a mapping. Other than the reversing of
pairs, a mapping is a transformation. S.S., Junior
Every transformation has a unique inverse. Since a
transformation is one-to-one and onto, it means that there is
exactly one element in A that that matches with one element in B.
So no matter if you are going to B from A or to A from B, there
will always be a corresponding element in the second set. [It's
kinda like "for every action, there is an equal and opposite
reaction.''] L.S., Junior
M.M. shows here that he has good command of the basic ideas in question 1;
not only are the definitions "similar,'' but in fact they are identical.
This was the point of the question. Similarly, in question 3,
L.S. demonstrates an understanding of the fact that all transformations are
invertible. Her response includes a nice description of a one-to-one
correspondence that students in class found a good explanation.
In question 2, however, S.S. reveals a less than complete understanding of
the definition of a transformation. Such a response offers many
opportunities in class: is there a difference in saying "every mapping is
not a transformation'' and "not every mapping is a transformation''? The
response includes some of the main ideas involving one-to-one and onto
functions; the lesson is that sometimes an imperfect response can provide
an excellent learning moment for the entire class, particularly if several
students shared in the difficulty. All three responses enabled us to have
a brief, but important, discussion of how important precise language is in
mathematics.
In reviewing the reading responses to these three questions, it was clear
before class that most students had a solid grasp of the material. A few
short minutes at the start of class were used to make certain the
terminology was clear to all, and from there we were able to quickly
develop more in-depth ideas related to the geometric concepts we were
studying with the Euclidean motions. Had class instead begun with the
question "What is the definition of a function?'', followed by introducing
the term "mapping'', and then "transformation,'' it is certain that a much
more lengthy segment of time would have been devoted to elementary review.
4.3 General Remarks on Student Responses
We have observed several unexpected trends while reading our students'
responses. First, students tend to be more verbose via email than they are
in handwritten exercises. Certainly a part of this is the ease of editing
and expanding their responses at the keyboard. Secondly, the lack of
mathematical symbols in email is actually a large advantage since it forces
the students to explain their thought process in prose. Finally, providing
another regular mechanism for communication gives students who are
typically quiet in class an outlet to express their insights and share them
with the rest of the class when their email is displayed at the beginning
of class.
5. Data from Student Responses to Supplementary Evaluations
In each class where this approach to reading assignments has been used, we
have conducted a supplementary anonymous evaluation to gain further student
feedback. The students were given four options
(1) Strongly disagree
(2) Disagree
(3) Agree
(4) Strongly agree
to respond to the statements:
The reading assignments were helpful in understanding the
course material.
The reading assignments were useful in preparation for
the class meetings.
The reading questions were helpful in
focussing my reading.
I would have regularly read the text before class without
the reading assignments.
Table 1. Mean Responses to Supplementary Evaluations
Term
Course
Q1 Understanding
Q2 Preparation
Q3 Focussing
Q4
Read without
Spring 97
Calculus I
2.9
3.0
3.0
n/a
Fall 97
Calculus I
3.2
3.3
3.2
n/a
Calculus II
2.8
3.0
3.2
n/a
Multivariable
2.8
3.3
3.2
n/a
Spring 98
Calculus II
3.2
3.2
3.5
1.9
Fall 98
Calculus I
3.1
3.2
3.1
2.3
Linear
3.2
3.2
3.4
1.7
Multivariable
3.3
3.4
3.4
2.1
Spring 99
Calculus II
3.1
3.3
3.4
2.1
Fall 99
Calculus II
3.0
3.1
3.2
2.0
Linear
3.1
3.3
3.1
2.0
Spring 00
Intro Stats I
3.2
3.2
3.2
2.1
Intro Stats II
2.9
3.1
3.1
2.3
Geometry
3.4
3.5
3.5
1.9
Table 1 demonstrates that on average, students agree with the statements
that the reading assignments were helpful in understanding course material,
even moreso in preparing for class meetings, and likewise in helping them
focus their reading. In addition, students generally disagreed with the
statement "I would have regularly read the text without the assignments.''
This data supports what has been our consistent experience with this
approach.
Not only did students believe that the reading assignments were a good
idea, they actually did the reading! The first column of Table 2 shows the
students' response to the question:
On average, how much time did you spend on each reading assignment?
(1) 0--15 mins
(2) 15--30 mins
(3) 30--45 mins
(4) 45--60 mins
(5) More than an hour
The latter two columns of Table 2 show the mean percent of respondents per
assignment and the median percent of assignments completed per student.
(We use the median to reduce the influence of the small number of outliers
who completed few of the assignments.)
Table 2. Time per Assignment
and Response Rates
Term
Course
Mean Time/ Student
Mean Response/
Assignment (%)
Median Completed/ Student (%)
Spring 97
Calculus I
2.5
82
86
Fall 97
Calculus I
1.9
74
88
Calculus II
1.8
78
88
Multivariable
2.2
73
70
Spring 98
Calculus II
2.0
82
88
Fall 98
Calculus I
2.0
80
89
Linear Alg
2.0
84
90
Multivariable
1.9
83
96
Spring 99
Calculus II
2.2
83
92
Fall 99
Calculus II
1.9
72
86
Linear Alg
2.0
75
86
Spring 00
Intro Stats I
2.6
82
83
Intro Stats II
2.8
82
92
Geometry
2.7
89
96
Overall, we observe that on average students spent about 30 minutes on a
given reading assignment. In addition, consistently at least 75% of each
class completed and responded to a particular set of questions. Moreover,
the final column indicates that for most students, the vast majority of the
overall collection of reading assignments was completed. These data,
together with the student comments regarding their opinion that the
exercises were effective, demonstrate the high level of student involvement
in this activity, and make plausible our claims that the efficiency of
class time was significantly improved. While we would prefer that every
student complete every reading assignment, we consider the approach very
successful when 80% of the students in an Introductory Statistics course
spend, on average, more than 30 minutes reading the text before the
material is discussed in class.
Finally, it is again students' own words that offer so much evidence
of their satisfaction regarding these assignments:
"I firmly believe I would not have read as thoroughly and would not
have been as prepared for class were it not for the reading
questions. They weren't a big deal to complete at all, and I feel
they were vital in my understanding of the course.'' --
Geometry
"I felt they were very helpful considering I tend to struggle with
math
courses. A very good idea!!'' -- Statistics
"Good stuff, helps to at least get a feel for the material before it
is covered, allows a slightly faster pace.'' -- Linear Algebra
"I felt the reading questions made me concentrate more on what I was
reading and (I) got more out of the reading than I otherwise would
have.''
-- Calculus II
"They were quite helpful. But it was sometimes frustrating if I
didn't
understand the material to have to wait until class to finally see
how
to do it.'' -- Calculus II
The last quote demonstrates what we are striving for: students who
are thinking about mathematics, working on mathematics, and cannot
wait to get to class.
6. Other Issues/Potential Pitfalls
There are some start-up costs to be aware of when using these
assignments. Writing the assignments can be a time-consuming affair, and we
have found that it is easiest to write several weeks, or a month, of
assignments at a time. This has required us to have our courses fairly
well-organized to assign specific readings this far in advance. One
advantage is that this has helped us keep a brisk pace in our courses and
keep up with our initial syllabus.
Text selection is extremely important when using these assignments since
the students will be reading the text as their first introduction to the
course material. The students' perception of the readability of the text,
as well as the choice of questions, can significantly affect their opinion
of the efficacy of the assignments. If the questions are simplistic, then
the students view the assignments as busy work; if the questions are too
difficult, then they add to the frustration that many students feel when
reading mathematics. Quite often, several semesters of minor adjustments
are required to fine-tune the questions.
We also feel that it is important to recognize that these reading
assignments add to the students' workload in the course. Since the
assignments keep the students engaged with the course material on a nearly
daily basis, they can serve a similar role to lengthy homework assignments.
It is important that these reading tasks not simply be added to the list of
things required of students, but that their addition is reasonably
accomodated in an overall vision for expectations of students.
There are, of course, problems that can arise when an assignment is
technology dependent, such as access to email, network outages, and student
apprehension about using the technology. Since network problems will
inevitably occur, we have told students that they can turn in their
assignments on paper before class if they have trouble accessing email the
night before the assignment is due. A bit of flexibility on the part of
the instructor seems sufficient to handle these minor challenges.
7. Conclusion
We find the overall atmosphere in our classes exciting with this approach.
Students read to learn mathematics . . . They explain their mathematical
ideas in prose . . . Discussions become more lively . . . The instructor
gets individual feedback on each student's understanding of concepts . . .
Class time is spent more efficiently . . . Deeper mathematics is considered
. . . Students even profess to like the assignments.
It sounds like everyone is winning! The approach has changed the
fundamental way we direct our students in learning mathematics, and does so
in a way with many important benefits. For all these reasons, we hope that
other instructors will join us in the endeavor. The reader is encouraged
to take a look at how an entire semester develops in this approach by
visiting our courses on the World Wide Web at
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Introduction to Quantitative Reasoning
This course is designed to develop students' ability to reason with quantities through solving problems in arithmetic, algebra, probability, statistics, logic and geometry. Students explore attitudes about and approaches to quantitative work, and learn effective study techniques. The course helps prepare students for the Q course requirement. May not be counted toward a major in Mathematics. May not be taken Pass/Fail.
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0
Binding:
Unknown Binding Textbook
Publisher:
PRENTICE HALL
Supplemental materials are not guaranteed for used textbooks or rentals (access codes, DVDs, workbooks).
Prentice Hall Mathematics: Courses 1, 2, and 3 2008 Course 2 Prentice Hall Mathematics Course 2:A structured approach to a variety of topics such as ratios, percents, equations, inequalities, geometry, graphing and probability.Test Taking Strategies provide a guide to problem solving strategies that are necessary for success on standardized tests. Checkpoint Quizzes assess student understanding after every few lessons. Daily Guided Problem Solving in the text is supported by the Guided Problem Solving worksheet expanding the problem, guiding the student through the problem solving process and providing extra practice. Prentice Hall Mathematics - Value Pack with textbook purchase add All-in-One Student Workbook Prentice Hall Mathematics maintains the quality content for which Prentice Hall is known, with the research-based approach students need. Daily, integrated intervention and powerful test prep help all students master the standards and prepare for high-stakes assessments.Features and Benefits Prentice Hall's unique Instant Check System™ is a built-in way to ensure that your students make progress every day. Green Means GO! Built-in help give students the green light to succeed. No other math program provides ongoing, embedded student support like Prentice Hall Mathematics. Throughout every lesson, "Go for Help" icons point the way to a helping hand. Differentiate Instruction with Ease— All Prentice Hall Mathematics resources are coded by Special Needs, Below Level, All Students, Advanced, and ELL. Adapted Student Resources help you meet every student's needs. Superior Planning, Teaching, and Assessment Tools — Spend less time planning, assessing, and grading — and more time teaching. Prentice Hall Mathematics supports you in all the ways you teach. Research and Validity Quantitative and qualitative research supporting Prentice Hall Mathematics programs. Find out more about Prentice Hall's approach to the foundational and efficacy research that supports our quality programs. Prentice Hall Research Overview PDF Icon * Prentice Hall Mathematics, Grades 612 * Math Success Tracker, Grades 68
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Limit - Research Article from Macmillan Science Library: Mathematics
Limit
The concept of limit is an essential component of calculus. Limits are typically the first idea of calculus that students study. Two fundamental concepts in calculus—the derivative and the integral—are based on the limit concept. Limits can be examined using three intuitive approaches: number sequences, functions, and geometric shapes.
Number Sequences
One way to examine limits is through a sequence of numbers. The following example shows a sequence of numbers in which the limit is 0.
The second number in the sequence, ½, is the result of dividing the first number in the sequence, 1, by 2. The third number in the sequence, ¼, is the result of dividing the second number in the sequence, ½, by 2.
This process of dividing each number by 2 to acquire the next number in the sequence is continued in order to acquire each of the remaining values. The...
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Sketchpad® Dynamic Geometry® software gives students a tangible, visual way to learn mathematics that increases their engagement, understanding, and achievement. And it's not just for geometry. Use it for elementary and middle school math, algebra, precalculus, and calculus Geometer's Sketchpadplot is a portable command-line driven interactive data and function plotting utility. It was originally intended as to allow scientists and students to visualize mathematical functions and data. It does...
Graph is an open source application used to draw mathematical graphs in a coordinate system. Anyone who wants to draw graphs of functions will find this program useful. The program makes it very easy to...
Geometry Pad is a dynamic geometry application for iPad and Android tablets. Geometry Pad is your personal assistant in teaching and learning geometry through practice. With the Geometry Pad you can create...
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7th Grade Math Details
Thinkwell's 7th Grade Math course includes thousands of automatically graded 7th Grade Math problems, printable worksheets for each topic and subchapter, and lots of animated interactivities, and at the core of this complete homeschool course are fun and effective video lessons that students love to use.
Thinkwell's homeschool video lessons feature Edward Burger, an award-winning teacher with a special talent for making math simple for any student. Your homeschool student will enjoy his sense of humor and his obvious passion for teaching math. Created to work with any learning style, his homeschool video lessons will keep your students engaged and entertained so they'll learn the fundamentals of math easily.
Thinkwell's 7th Grade Math has all the features your home school needs:
The number of contact hours in a course reflects the amount of time a student will typically spend completing the assignments in each course (i.e. watching videos, doing exercises, taking exams, etc...). Many people think about contact hours as the "seat time" for a course. Thinkwell provides this information so you can ensure that the amount of instruction in a Thinkwell course meets the standards and requirements for your state or region.
Automatically graded 7th grade math tests, including 12 chapter tests, as well as practice tests, a midterm, and a final exam
Real-world application examples in both lectures and exercises
Glossary of more than 200 mathematical terms
Closed captioning for all video lessons (most are also available in Spanish)
Brand-new content to help students advance their mathematical knowledge:
operations with rational numbers (fractions and decimals)
operations with integers
solving equations and inequalities
rates, ratios, percent, and proportions
square roots
Pythagorean theorem
bar graphs, histograms, box-and-whisker plots, and line graphs
scatter plots
lines, angles, and polygons
transformations, dilations, and symmetry
perimeter and area of polygons
circumference and area of circles
volume and surface area of prisms, cylinders, pyramids, and cones
experimental and theoretical probability
probability of independent and dependent events
permutations and combinations
About the Author
Edward Burger Williams College listed him in the "100 Best of America". After completing his tenure as Gaudino Scholar at Williams, he was named Lissack Professor for Social Responsibility and Personal Ethics. In 2010, he won the prestigious Robert Foster Cherry Award for Great Teaching.
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas andThinkwell wants you to be sure that this is the right course for your family. Not only do we provide a FREE 2-week trial, but we'll also refund your money within 3 business days of purchase, for any reason. And if your children end up in the wrong math grade level, we're happy to move them to the correct course within the first 2 weeks after you activate your subscription.
Thinkwell is proud to have received the Pioneer Award from the Education Innovation Network for having been recognized as "Best In Class" at their 2010 Summit.
"The 'Best In Class' designation identifies the cream of the crop of companies truly employing innovation to further the cause of improving education."
- Michael Moe, Summit Co-organizer
A+ Reliability Rating
The Better Business Bureau has given Thinkwell their highest rating, an A+.
"The grade represents BBB's degree of confidence that the business is operating in a trustworthy manner and will make a good faith effort to resolve any customer concerns filed with BBB."
- from the BBB website
Used by
Johns Hopkins University Center for Talented Youth
The Center for Talented Youth at Johns Hopkins University has used Thinkwell courses as the primary "textbooks" in their programs since 2000.
We're very honored by the fact that they use us in every subject matter that we make a course for.
We have enjoyed our partnership with them, and the families we've met through the Center for Talented Youth program, immensely.
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In
order to become effective citizens, workers, advocates --indeed in
order to perform a great variety of roles-- students must become competent in
using and reading quantitative data, in understanding quantitative evidence and
in applying basic quantitative skills so that they can solve real life problems.Such skills are usually taught through work in mathematics and statistics
courses, but they can be taught more effectively through work in courses within
the studentsí chosen major (or minor) discipline.A program that involves quantitative reasoning across the curriculum
gives students the opportunity to learn the broad significance and applicability
of quantitative reasoning in the particular subjects that are meaningful,
important and interesting to them.
The
Quantitative Reasoning Requirement at Hollins
In
2001 Hollins University implemented a two part Quantitative Reasoning program
consisting of a QR Basic Skills requirement and an QR Applied Skills requirement.This program will ensure that all Hollins graduates have not only a
mastery of basic quantitative reasoning skills but also an appreciation for how
these skills apply to the liberal arts curriculum.
The
QR basic skills requirement is designed to help students gain an understanding
of fundamental mathematical skills that they need to be successful in courses
that require quantitative reasoning.The
basic skills requirement can be satisfied by achieving a satisfactory score on
the Quantitative Reasoning Assessment (given to new students every fall) or by
passing Mathematics 100, Introduction to Quantitative Reasoning.This basic skills requirement is a prerequisite for all courses
satisfying the QR applied skills requirement and must be completed by the end of
each studentís sophomore year.A
student who has satisfied the QR basic skills requirement will demonstrate a
baseline understanding of various quantitative topics (algebra, graphing,
geometry, data analysis and linearity).
The
applied skills requirement is designed to provide students with the opportunity
to apply mathematical and quantitative skills as they solve problems in their
chosen disciplines.The applied
skills requirement can be satisfied by passing a course designated as a QR
applied course.Our goal is for
students to choose a QR applied course in their major or minor field.A QR applied course should involve students in the application of
quantitative skills that arise naturally in the course, in a way that advances
the goals of the course and in a manner than is not merely a rote application of
a mathematical procedure.Writing,
student collaboration and thoughtful use of instructional technology all have
important places in a QR applied course.
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algebra-based Introductory Statistics courses. Offering the most accessible approach to statistics, with a strong visual/graphical emphasis, this text offers a vast number of examples on the premise that students learn best by "doing". The fourth edition features many updates and revisions that place increased emphasis on interpretation of results and critical thinking in addition to calculations. This emphasis on "statistical literacy" is reflective of the GAISE recommendations. Datasets and other resources (where applicable) for this book are available here.
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Practise for your exam on the offical National 5 specimen paper from the Scottish Qualifications Authority. Plus each book includes additional model papers and extra revision guidance, making them an essential purchase for any student.; Discover how to get your best grade with answers checked by senior examiners.; Prepare for your exams... more...
Model Answers in Ordinary National Certificate Mathematics for Engineers presents a series of model answers that include all the topics covered by the many different syllabuses in Mathematics for the Ordinary National Certificate in Engineering. This book is composed 16 chapters; each chapter contains Worked Examples, Hinted Examples, and Further... more...
LearningExpress's 20 Minutes a Day guides make challenging subject areas more accessible by tackling one small part of a larger topic and building upon that knowledge with each passing day. Practical Math Success in 20 Minutes a Day features: ? A walkthrough of the fundamental concepts of pre-algebra, algebra, and geometry ? Hundreds of practice... more...
Solutions to the 25th & 26th International Young Physicists' Tournament provides original, quantitative solutions in fulfilling seemingly impossible tasks. The book expands on the solutions required by the problems. Many of the articles include modification, extension to existing models in references, or derivation and computation based on fundamental... more... The book will be invaluable for... more...
This book is for adult learners who wish to undertake a self-study program in preparation for the GED Mathematics exam. This guide offers a review of all tested topics on the Mathematics section of the GED and a brush up on basic study and test-taking skills. Inside is targeted instruction based on past GEDs, with practice on the basics including:... more...
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal... more...
Along with more than 2100 integral equations and their solutions, this handbook outlines exact analytical methods for solving linear and nonlinear integral equations and provides an evaluation of approximate methods. Each section provides examples that show how methods can be applied to specific equations. more...
A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and consider California High School Exit Exam: Mathematics can help you pass this critical competency exam necessary for... more...
| 677.169 | 1 |
Carnegie Learning, a leading publisher of core and supplemental mathematics programs, was founded by cognitive and computer scientists in conjunction with practicing math teachers, and provides innovative research-based math curricula for middle and high school
| 677.169 | 1 |
In the past 50 years, discrete mathematics has developed as a far-reaching and popular language for modeling fundamental problems in computer science, biology, sociology, operations research, economics, engineering, etc. The same model may appear in different guises, or a variety of models may have enough similarities such that same ideas and techniques you?re an academic or a practitioner, a sociologist, a manager, or an engineer, one can benefit from learning to think systemically.?Problems (and messes) are everywhere and they?re getting more complicated every day.?How we think about these problems determines whether or not we?ll be successful in understanding and addressing them.?This book... more...
With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as... more...
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined... more...
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite... more...
| 677.169 | 1 |
Calculus for Dummies
Each year, one million high school and college students struggle through calculus, the single toughest maths class that most people will ever take. ...Show synopsisEach year, one million high school and college students struggle through calculus, the single toughest maths class that most people will ever take. With easy-to-understand explanations, memorable examples, and helpful shortcuts, math teacher Mark Ryan takes the mystery out of calculus concepts and problems - everything from limits, derivatives, and integration to word problems, integral theorems, and conic sections. He grounds calculus in the real world, showing why it's a key problem-solving tool in most scientific and technical fields. Complete with handy reference tables and formulas, this is a classroom companion for calculus students everywhere.Hide synopsis
Description:Fair. NO CD; No Access Code; very small hole through back cover...Fair. NO CD; No Access Code; very small hole through back cover and about 15 pages; Some delamination and curling; Some highlighting, markings, tears, scratches, creases, discoloration and wrinkling; Significant edge, cover and corner wear; Unless stated otherwise herein the notes, complementary books or items are not present; $20.00 minimum excluding shipping for orders to Puerto Rico & Hawaii; standard shipping is by USPS Media Mail & Expedited shipping is by USPS Priority Mail or equivalent;
Reviews of Calculus for Dummies
This difficult to understand branch of math was first introduced to me in a two year college as a REVIEW. Needless to say, I didn't get very far. Neither did the rest of the class except ONE (brilliant) student.
This text is excellent in its presentation, both in text and graphics. I wish this had been my textbook for the class!
I was in a jugle, a deep, dark, frightening jungle. The jungle of CALCULUS. Suddenly a light came in front. A subtle, fagile one but growing even larger and larger as I slowly crawled towards the middle of this book. Now I walk more confident, steping firmly with a backbone for dummies:-) I strongly recomend this book to everyone who have entered the financial area with weak mathematical
| 677.169 | 1 |
This is a lesson created for fifth grade, but can be modified to fit other grade levels. The assignment is based on a real...
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This is a lesson created for fifth grade, but can be modified to fit other grade levels. The assignment is based on a real world task of ordering food and following a budget. The objective is for students to compute the total of the dinner without using a calculator. The lesson outlines all of the steps necessary for this assignment.
This site has some great geometry worksheets for high school level students. There are free worksheets as well as an option...
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This site has some great geometry worksheets for high school level students. There are free worksheets as well as an option to buy more worksheets with study resources. The worksheets are fun and use engaging examples to explain concepts.
This fall I will be teaching a new course entitled "Applied Mathematics" which is intended for students who demonstrate a...
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This fall I will be teaching a new course entitled "Applied Mathematics" which is intended for students who demonstrate a need to reduce the Algebra II requirement in the Michigan Merit Curriculum due to academic difficulty in Algebra I and/or Geometry. The course features interwoven strands of algebra and functions, statistics, and probability, with a focus on applications of mathematics. Students will learn to recognize and describe important patterns that relate quantitative variables and develop strategies to make sense of real-world data. The course will develop students' abilities to solve problems involving chance and to approximate solutions to more complex probability problems by using simulation. The goal that will be addressed in this lesson is to review Algebra I fundamentals, more specifically mathematical models (price-demand model, formulas as models, and operations with real numbers) to lay the foundation for the semester.
This is a lesson plan for solving systems of linear equations to Algebra 1 students. Methods to be taught include...
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This is a lesson plan for solving systems of linear equations to Algebra 1 students. Methods to be taught include substitution, elimination, and graphing. The lesson also includes the use of graphing calculators and spreadsheets to solve systems of equations. The lesson involves practice with real world application problems, as well as creation and presentation of original problems by students.
The goal for this lesson is to provide students with an understanding of how to find the area of any regular polygon. This is...
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The goal for this lesson is to provide students with an understanding of how to find the area of any regular polygon. This is a discovery-based lesson in which students collaborate with their peers and test ideas using technology.
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The goal that will be addressed during this lesson plan is to provide the concepts, methods, and tools for understanding characteristics and transformations of graphs from their parent functions using a goal-directed instructional design plan.
This lesson plan was developed to help early grade school teachers demonstrate to students how to use simple deductive logic...
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This lesson plan was developed to help early grade school teachers demonstrate to students how to use simple deductive logic to solve a simple 4x4 matrix Sudoku puzzle. There is a description of instructional objectives as they apply to the NET-S and to the Michigan Grade level Content Expectations. There is a description of important content for the learner to grasp in order to complete the objectives. There is a PDF of an example puzzle to use as practice or assessment. There is a link to developmentally appropriate puzzle web sites to be used as practice or assessment. Finally, there is a brief description of an instructional plan.
| 677.169 | 1 |
3-12
Remote Sensing Math is a complete study for remote sensing and mathematical models. Each lesson in this guide is a supplement for teaching mathematical topics. The problems can be used to enhance understanding of the mathematical concept or as an assessment of student mastery.
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About the book:
Sobel and Lerner aim to provide teachers with a teachable text and students with a readable one that will properly prepare them for future courses, particularly calculus. The text is designed specifically to ease the transition to calculus and directly involve graphing calculators. The book features: special material devoted to directly supporting topics in precalculus without covering the actual topics themselves; over 500 display examples that demonstrate and support mathematical developments; and optional graphing calculator sections with exercises, sometimes to verify what has been done by hand, other times to produce graphs of more complicated equations, observations and analysisBack Alley Books via United States
Hardcover, ISBN 0132991241 Publisher: Prentice-Hall, 1995 ****Instructorâ??s Edition / Same as Student Version but may contain additional notes or answers. May have tape on cover. ***New Book / Never Used*** May not include supplements such as CDs infotrac or other web access codes. Quick shipping.
Hardcover, ISBN 0132991241 Publisher: Prentice Hall College Div, 1995 5th ed.. Hardcover. . 5th ed.
Hardcover, ISBN 0132991241 Publisher: Prentice Hall College Div, 1995
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Hardcover, ISBN 0132991241 Publisher: Prentice Hall, 1995 College Div, 1995 0132991241 Publisher: Prentice Hall College Div, 1995 College Div, 1995-Hall, 1995 Good. US Edition. May include moderately worn cover, writing, markings or slight discoloration. SKU:9780132991247 0132991241 Publisher: Prentice Hall College Div, 1995
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Mathematical programming is used to find the best or optimal solution to a problem that requires a decision or set of decisions about how best to use a set of limited resources to achieve a state goal of objectives.
Steps involved in mathematical programming
Conversion of stated problem into a mathematical model that abstracts all the essential elements of the problem.
Exploration of different solutions of the problem.
Finding out the most suitable or optimum solution.
Linear programming requires that all the mathematical functions in the model be linear functions .
Blending problems refer to situations in which a number of components (or commodities) are mixed together to yield one or more products.
Typically, different commodities are to be purchased. Each commodity has known characteristics and costs.
The problem is to determine how much of each commodity should be purchased and blended with the rest so that the characteristics of the mixture lie within specified bounds and the total cost is minimized .
A manufacturer knows that he must supply a given number of items of a certain product each month for the next n months.
They can be produced either in regular time, subject to a maximum each month, or in overtime. The cost of producing an item during overtime is greater than during regular time. A storage cost is associated with each item not sold at the end of the month.
The problem is to determine the production schedule that minimizes the sum of production and storage costs .
The variety of situations to which linear programming has been applied ranges from agriculture to zinc smelting.
Steps Involved:
Determine the objective of the problem and describe it by a criterion function in terms of the decision variables.
Find out the constraints.
Do the analysis which should lead to the selection of values for the decision variables that optimize the criterion function while satisfying all the constraints imposed on the problem.
12.
Developing LP Model (2) Example: Product Mix Problem The N. Dustrious Company produces two products: I and II. The raw material requirements, space needed for storage, production rates, and selling prices for these products are given in Table 1 . The total amount of raw material available per day for both products is 15751b. The total storage space for all products is 1500 ft 2 , and a maximum of 7 hours per day can be used for production.
13.
Developing LP Model (3) Example Problem All products manufactured are shipped out of the storage area at the end of the day. Therefore, the two products must share the total raw material, storage space, and production time. The company wants to determine how many units of each product to produce per day to maximize its total income. Solution
The company has decided that it wants to maximize its sale income, which depends on the number of units of product I and II that it produces.
Therefore, the decision variables, x 1 and x 2 can be the number of units of products I and II, respectively, produced per day.
subject to the constraints on storage space, raw materials, and production time.
Each unit of product I requires 4 ft 2 of storage space and each unit of product II requires 5 ft 2 . Thus a total of 4x 1 + 5x 2 ft 2 of storage space is needed each day. This space must be less than or equal to the available storage space, which is 1500 ft 2 . Therefore,
4X 1 + 5X 2 1500
Similarly, each unit of product I and II produced requires 5 and 3 1bs, respectively, of raw material. Hence a total of 5x l + 3x 2 Ib of raw material is used.
This must be less than or equal to the total amount of raw material available, which is 1575 Ib. Therefore,
5x 1 + 3x 2 1575
Prouct I can be produced at the rate of 60 units per hour. Therefore, it must take I minute or 1/60 of an hour to produce I unit. Similarly, it requires 1/30 of an hour to produce 1 unit of product II. Hence a total of x 1 /60 + x 2 /30 hours is required for the daily production. This quantity must be less than or equal to the total production time available each day. Therefore,
x 1 / 60 + x 2 / 30 7
or x 1 + 2x 2 420
Finally, the company cannot produce a negative quantity of any product, therefore x 1 and x 2 must each be greater than or equal to zero.
An equation of the form 4x 1 + 5x 2 = 1500 defines a straight line in the x 1 -x 2 plane. An inequality defines an area bounded by a straight line . Therefore, the region below and including the line 4x 1 + 5x 2 = 1500 in the Figure represents the region defined by 4x 1 + 5x 2 1500 .
Same thing applies to other equations as well.
The shaded area of the figure comprises the area common to all the regions defined by the constraints and contains all pairs of x I and x 2 that are feasible solutions to the problem.
This area is known as the feasible region or feasible solution space . The optimal solution must lie within this region .
There are various pairs of x 1 and x 2 that satisfy the constraints such as:
This indicates that maximum income of $4335 is obtained by producing 270 units of product I and 75 units of product II.
In this solution, all the raw material and available time are used, because the optimal point lies on the two constraint lines for these resources.
However, 1500- [4(270) + 5(75)], or 45 ft 2 of storage space, is not used. Thus the storage space is not a constraint on the optimal solution; that is, more products could be produced before the company ran out of storage space. Thus this constraint is said to be slack .
If the objective function happens to be parallel to one of the edges of the feasible region, any point along this edge between the two extreme points may be an optimal solution that maximizes the objective function. When this occurs, there is no unique solution, but there is an infinite number of optimal solutions.
The graphical method of solution may be extended to a case in which there are three variables . In this case, each constraint is represented by a plane in three dimensions, and the feasible region bounded by these planes is a polyhedron.
Examine each boundary edge intersecting at this point to see whether movement along any edge increases the value of the objective function.
If the value of the objective function increases along any edge, move along this edge to the adjacent extreme point. If several edges indicate improvement, the edge providing the greatest rate of increase is selected.
Repeat steps 2 and 3 until movement along any edge no longer increases the value of the objective function.
23.
The Simplex Method (3) Example: Product Mix Problem The N. Dustrious Company produces two products: I and II. The raw material requirements, space needed for storage, production rates, and selling prices for these products are given below: The total amount of raw material available per day for both products is 15751b. The total storage space for all products is 1500 ft 2 , and a maximum of 7 hours per day can be used for production. The company wants to determine how many units of each product to produce per day to maximize its total income.
Introducing these slack variables into the inequality constraints and rewriting the objective function such that all variables are on the left-hand side of the equation. Equation 4 can be expressed as:
It is now obvious from these equations that the new feasible solution is:
x 1 = 315, x 2 = 0, S 1 = 240, S 2 = 0, S 3 = 105, and Z = 4095
It is also obvious from Eq.(A2) that it is also not the optimum solution . The coefficient of x 1 in the objective function represented by A2 is negative ( -16/5), which means that the value of Z can be further increased by giving x 2 some positive value.
Step VI: Check for optimality. The second feasible solution is also not optimal, because the objective function (row A2) contains a negative coefficient. Another iteration beginning with step 2 is necessary .
In the third tableau (next slide), all the coefficients in the objective function (row A3) are positive. Thus an optimal solution has been reached and it is as follows:
The simplex solution yields the optimum production program for N. Dustrious Company.
The company can maximize its sale income to $4335 by producing 270 units of product I and 75 units of product II.
There will be no surplus of raw materials or production time .
But there will be 45 units of unused storage space .
The managers are interested to know if it is worthwhile to increase its production by purchasing additional units of raw materials and by either expanding its production facilities or working overtime .
Sensitivity analysis helps to test the sensitivity of the optimum solution with respect to changes of the coefficients in the objective function, coefficients in the constraints inequalities, or the constant terms in the constraints.
For Example in the case study discussed:
The actual selling prices (or market values) of the two products may vary from time to time. Over what ranges can these prices change without affecting the optimality of the present solution ?
Will the present solution remain the optimum solution if the amount of raw materials, production time, or storage space is suddenly changed because of shortages, machine failures, or other events?
The amount of each type of resources needed to produce one unit of each type of product can be either increased or decreased slightly. Will such changes affect the optimal solution ?
Because x j ' and x j '' can have any nonnegative values their difference (x j ' –x j '') can have any value (positive or negative). After substitution, the simplex method can proceed with just nonnegative variables.
Since the market value (or selling price) of 1 unit of product I is $13 and it requires 4 ft 2 of storage space, 5 lbs of raw materials, and 1 minute of production time, the following constraint must be satisfied:
4y 1 + 5y 2 + 5y 3 13
Similarly, for Product II:
5y 1 + 3y 2 + 2y 3 11
In addition, the unit prices y 1 , y 2 and y 3 must all be greater than or equal to zero.
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Teaching algebra is quite demanding and difficult for both the new teacher and the students. Confidence is a great help. The following suggestions will help build success based on being confident, thorough, and thoughtful.
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Steps
1
Attend school district training to get copies of teaching suggestions and example assignments for the the first unit. Often algebra will receive more assignments from the district math consultants (they're not strictly supervisors, but advisers of sorts) as some kind of academic math coordinators, or services persons.
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2
Use the school district's scope and sequence materials or manual which tells you what to teach and when, and how many days to spend on various topics.
Realize that the district produced scope and sequence usually does not go straight through the book and has extra assignments, that may not need.
3
Read over the publisher's similar kind of scope and sequence, which goes straight through the book and has some "extra" materials.
4
Prepare or obtain a syllabus to give to the students that covers the subject.
5
Make a lesson plan. Introduce the topic, demonstrate, use student centered guided practice in classroom work sessions; perhaps using groups may work for you.
6
Teach students using algebra concepts that are well ordered and clarified. Review and reteach a little bit each day, which can be woven into the introduction of each days topic; perhaps, you use a strategy somewhat like the following:
"As we saw yesterday this is _____ and recently this was ____ like ____". and then:
"Today we are extending those ideas into _____". "For example: _______..."
"We'll do some guided practice; now here is that assignment: ____."
"You will get into groups for this ____." (sometimes for appropriately complex kinds of work, such as to: produce a pattern, a sketch, a chart, list of x,y data a co-ordinates, a description, an expression, or an equation, a relation, or a function, etc.).
7
Do not "teach the book"; rather, teach the students the key concepts and expand on them. While the text is an important tool and reference, you'll want to "unlock the topic" and teach the students through your own knowledge of the subject, using the book for some materials, lessons and as a guide, source of many problems and exercises for assignments.
8
Lecture less, but guide and facilitate more. Use some special real world activity for each unit which may gather data, sometimes surveying or doing some kinds of experiments.
9
Use math vocabulary all the time with some restating using simpler terms, but not just the simple words, so students will know that you think the vocabulary is important.
10
Teach algebraic thinking, using multiple representations: using patterns of growth or decay, using data, visual sketch, graphing, and expressing either a relation or a function.
11
Explore examples of math in the real world (slope, roof pitch, percent hill grades) and other of such things also in everyday life (area, volume, cubic yards of soil, sand or concrete) and in sports (statistics), math that is used for various jobs, etc.
12
Have answers when some students argue that math is useless and doesn't have anything to do with everyday life. Say that:
"It helps you have options/choices in life, including college. You have to take one or two math courses for almost any degree in college."
"It is needed in the military to pass tests for technical work."
"You never know whether you will end up in some kind of technical work where math is needed."
"You will need math to help your children and grandchildren with their school lessons."
"Math describes the real world with stunning accuracy using repeatable methods. In the words of Galileo, 'Mathematics is the language with which God has written the universe.'"
"Math is fundamentally the study of patterns, many of which are beautiful in themselves. Sometimes, math is useful much as art is useful.
13
Motivate students to do homework, by using it as a small part of the grade. Some small extra credit homework system may help.
14
Use "hands-on" activities planned for each major unit. Math needs to not only be abstract, but practical. Engage students in learning by providing manipulative activities that get students moving about, or manipulating math objects.
Use a classroom "algebra-football field" to have the students walk through to explain the movements on a number line and for graphing of positive and negative integers (zero at what would usually be the 50 yard line) or make quadrants, with (0,0) at the origin, etc.
Get someone to demo a graph, by shaping the arms, or tilting their arms to show slope. At the front of the room, so that some do not see it backward.
15
Test only what is taught. Make students accountable by testing as needed and as required by the school district and by the state. Also, occasionally use some short quizzes.
16
Reteach with a review and retest if needed, but do it while trying to keep making some progress on new materials.
17
Express happiness about students' small successes when they have the "Eureka moment!" or the "I got it!" Also, praise positive actions saying, "This is so cool! It's great. Hey, everybody is on task, being productive, practicing!
Keep being enthusiastic and showing joy about the students and math: "Yeah, you got it" "All right!" "Yeah!"
Be on! Be kind, and cleverly clap and say "Wow!" about the class getting it. Let students see, hear and believe that math is especially cool, exciting and fun -- to you (don't ever act like you're a substitute teacher, going through the motions. Do "not" say that you are "bored, hating school, or dull").
Represent, sale and promote school and the subject.
Classroom Procedures
1
Post just a few class rules, about 5 or 6, not twenty. Tell them that you will decide questions about rules, but that you try to be consistent and fair.
2
Teach classroom procedures for daily events such as roll call and tardies that do not take much time. Restrict hall passes to urgent use, not for going to lockers and such.
Teach management processes as they come up, such as: how group-work is conducted, papers are to show work, papers are to be headed and turned in, and so on -- all these are procedures, not rules.
3
Calculators can be a help or a hindrance, and are useful, but some uses of the calculator are too advanced while students are learning the basic principles.
4
Check out and get back calculators which will require a carefully planned and executed system to be accountable.
Use a visual check at a glance that proves that the calculators are all there. Just keeping them in an ordinary box is not effective.
One system is a hanging set of shallow pockets so that the screen shows above the pocket (this can be ordered on the internet) where the calculator covers are removed and put away, or someone may swipe calculators and leave only the covers, and it is not obvious at a glance.
Another system is a box with 30 to 40 numbered slots.
5
Teach from bell to bell, of course that includes guided practice -- but does not mean long lectures. Involve the students in math. That also means no free time and no free class periods in general.
You can have an in class math project (perhaps in groups) with gathering data and posters for exhibit, for something "fun" and engaging.
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Tips
It is very crucial to have students use the same calculator every time or they will remove batteries and punch the screens, and trash them and you would hardly catch the tricksters.
The textbook publisher usually puts out some extra work in worksheet form and perhaps you can have access to these. If you make some of your own worksheets, the publisher material may help so you can cut and paste copies on paper or on screen.
Develop a kind of "Math Olympics Day" with gathering data, measuring, drawing, graphing and calculating -- for finding and using a relation and seeing if it is a function, set parameters for x, and y.
Warnings
Worksheets usually do not cover the subject well. They skip around.
Understanding vocabulary to be able to interpret and decide what to do to answer a question and solve a problem can be the key to doing well on testing.
Copied assignments can be useful, but be sure your class is not a "worksheet mill" where you give odds and ends of worksheets
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Chris Tsuji Mathematics
Guidelines For Papers that you turn in.
Middle of top line: Short description of what is being turned in. Quiz 2. Assignment 2. This is the heading. This is what you want recorded.
Skip one lines.
Write the page and problems numbers assigned, if appropriate.
Skip two line
Identify the page being done by writing the page, circled, in the left margin.
Start the problem, one inch from the left margin with the problem number clearly identified.
Show all work downward. Be sure that the problem number and problem are separated.
Example: Assignment 2
page 23, 1, 3, 5, 7,10
page 23: 1) Simplify
4 + 3 - 2 7 - 2 5
Answers are on a separate line below all work. Circle all answers
Skip two lines between problems.
More than one paper, please staple together, top left corner, with page one on top. The staple should not cover any problems or work. When you staple, be sure the staple does not cover the heading nor any work.
* Work must be neat. Use both side of the paper if desire. * Copy enough of the problem so that someone that looks at your paper will understand the problem, then show work in one or two vertical columns (not across). * Answers only are not acceptable. * Number each problem clearly and indent work so that the problem and work can be easily found. * Separate each problem from the previous problem with two lines. Do not crowd your work. * Leave a one inch margin on the left. * Use equal signs, = with equations only. * If you have an answer, circle. * All answers are below the work and on a separate line. * Graphs must be done on graph paper. One square = one unit. * Show all work neatly downward, and neat for full credit.
IDENTIFICATION!
Fold the paper in half with heading inside. Place the fold on the left. Write your name, one inch from the fold, 2 inches below the top. Below your name, write your ordered pair in parentheses. Be sure that you plan the space for your name and ordered pair.
When you use a calculator, show all intermediate values. Example: 14 ÷ 6 + 4 2.33 + 4 6.33
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Understanding Elementary Algebra With Geometry - A Course for College Students - With CD - 6th edition
Summary: "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to t...show morehem at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples -- both numerical and algebraic--helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a variety of situations. This author team carefully prepares students to succeed in higher-level mathematics. ...show less
Types of Equations. Solving First-Degree Equations in One Variable and Applications. More First-Degree Equations and Applications. Types of Inequalities and Basic Properties of Inequalities. Solving First-Degree Inequalities in One Variable and Applications.
Book shows minor use. Cover and Binding have minimal wear, and the pages have only minimal creases. Free State Books. Never settle for less.
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0534999727 Item in very good condition and at a great price! Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!!
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Companion Products
Product Description
The LFBC Math program is a solid one, beginning with the knowledge that God created everything, and, because of this, order has resulted. It teaches that students can expect exactness, preciseness, and completeness in arithmetic/mathematics, just as they can expect it in God's creation. We start with the basic facts. Strong emphasis is given to learning the multiplication tables early. Later we proceed to the more complicated and abstract concepts in the upper grades.
Topics covered in Grade 12 include:
Preparing a Budget
Doing Income Tax
Balancing a Checkbook
Writing Checks
Tithing
Faith Promise Giving
Percentage of Profit
Life Insurance
Health Insurance
Buying a Car
Credit
and much more
Set include:
Studyguide: All materials for the student's academics, including text and activity questions
Studyguide Answers: Contains answers for the studyguide
Weekly Quizzes
Weekly Quiz Answers
Quarter Tests: Students take a test at the end of each 9-week periodi
Quarter Test Answers
All Scripture used in the curriculum is taken from the King James Version.
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The proper approach depends on your goals. If you are good and want to get better, that requires one technique. If you are intimidated by Math and you have always struggled, that requires a different method
| 677.169 | 1 |
A short article designed to provide an introduction to field theory and polynomials. Field theory looks at sets, such as the real number line, on which all the usual arithmetic properties hold, including, now, those of division. The study of multiple fields through Galois theory is important for the study of polynomial equations, and thus has applications to number theory and group theory. Applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.
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More About
This Book
Editorial Reviews
School Library Journal
Gr 5-10-- An excellent book in every way. The mathematical principles are enrichment-level concepts, clearly explained with text and illustration. Adler introduces ancient number theory principles and formulas on the most modern of inventions, the home computer; students will move ahead quickly with his carefully laid computer programming foundation. The illustrations are crucial to the concise text, with flow charts, tables, checker arrangements, and geometric figures. It's a simple book, and that's its beauty. Younger children will enjoy the large format, and those who have access to computers will find their knowledge of them extended with instruction in a little Basic programming while conveying fascinating number facts. Books like this nurture children, and it should be considered in spite of its limited appeal. --Kathleen Riley, Hilltop Elementary School, Beachwood, OH
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Calculus: A free calculus textbook courtesy of Wikibooks! Unfortunately its explanations are brief and the exercises are very limited. Perhaps in the future it will be as good as a commercial text. An improved book, in the public domain like this one, would save students a pretty penny! Use it to review Calculus topics if you do not have easy access to a Calculus book.
Leonard Euler: A short biography of the most prolific mathematician of all time. He was one of the most prolific mathematicians of all time. We will study Euler's Method—a procedure for numerically solving a first order differential equation.
Willard Libby: He won the Nobel Prize in chemistry in 1960 for his method of dating organic material by measuring the radioactive decay of carbon-14. His method uses an exponential model for radioactive decay as he mentions in his presentation speech: The disintegration [of Carbon-14] is such a slow procedure, however, that 5,600 years are required to convert half of these atoms into nitrogen. After another 5,600 years, there is still one quarter left, and after an equally long period of time one eighth, etc. Carbon-14 is thus said to have a half-life of 5,600 years.The presentation speech found at the link gives a good explanation of his work. Libby's very readable Nobel speech is also available on this web page.
Thomas Malthus: In his An Essay on the Principle of Population Malthus proposed an exponential model for the growth of human populations and discusses the negative effect of such a model on human happiness. His paper helped Charles Darwin and Alfred Wallace, independently, to develop the theory of natural selection.
Jules Verne's From the Earth to the Moon: An etext version of Jules Verne's novel. In the novel, the Gun Club sends a manned projectile to the moon. We will compute the earth's escape velocity by doing the "incontrovertible calculations" that Barbicane, president of the Gun Club, alludes to at the end of Chapter 2. At the end of Chapter 11, Barbicane chooses Tampa Town for the firing of the Gun Club's moon shot! A historical marker at the spot of the fictional launch can be found at Ballast Point in Tampa.
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free textbook offered by BookBoon.'This book and its companion (part II) present the elements of analysis and...
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This is a free textbook offered by BookBoon.'This book and its companion (part II) present the elements of analysis and linear algebra used in financial models and in microeconomics. Functions of one and several variables and matrices are developed in part I and vector spaces, linear mappings and optimization methods are developed in part II. Instead of formal proofs as in mathematical books, we develop examples and economic illustrations of the use of the concepts presented in the book. The books complement "Probability in Finance" and "Stochastic Processes in Finance" providing a broad overview of the mathematics of financial models.'
This course will be beneficial if you wish to learn how to communicate with the sounds and music of American English. The...
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This course will be beneficial if you wish to learn how to communicate with the sounds and music of American English. The purpose is not to increase your vocabulary, nor to improve your grammar, but to deal with the sounds of the words that you speak. Your message is of primary importance, but it may not be understood if your pronunciation is imprecise, inconsistent, or regional. This course is particularly useful for actors or for others who need to speak to diverse audiences, such as when giving a business presentation.You will have the flexibility of time to experience, at your own pace, aural and visual aspects of a sound. Within the course, students are assessed on their ability to recognize each sound in a variety of contexts and are given feedback on their particular answers.You will learn to:Articulate sounds and words using the dialect of Standard American English.Listen and think in terms of symbols for sounds, using the International Phonetic Alphabet.Use the International Phonetic Alphabet to transcribe from the Roman alphabet into the forty-four sounds of Standard American Dialect and vice versa.Analyze texts for phrasing, operative words, intonational patterns, degrees of stress.Achieve a proper use of weak forms for certain parts of speech in the English Language, making your speech clear and efficient.
The Boundless Accounting textbook is a college-level, introductory textbook that covers the subject of Accounting, core to...
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The Boundless Accounting textbook is a college-level, introductory textbook that covers the subject of Accounting, core to all studies of business. Boundless works with subject matter experts to select the best open educational resources available on the web, review the content for quality, and create introductory, college-level textbooks designed to meet the study needs of university students.This textbook covers:Accounting -- What is Accounting, The Accounting Concept, Overview of Key Elements of the Business, Conveying Accounting Information, Conventions and StandardsAccounting Information and the Accounting Cycle -- Basics of Accounting, The Accounting CycleFinancial Statements Overview -- The Income Statement, The Balance Sheet, The Statement of Cash Flows, Special Considerations for Merchandising CompaniesControlling and Reporting of Cash and Receivables -- Overview of Cash, Managing Cash, Overview of Receivables, Notes Receivable Detail, Basics of Receivables Management, Reporting and Analyzing ReceivablesControlling and Reporting of Inventories -- Understanding Inventory, Controlling Inventory, Valuing Inventory, Detail on Using LIFO, Additional Topics in Inventory Valuation, Assessing Inventory Management, Reporting and Analyzing InventoriesControlling and Reporting of Real Assets: Property, Plant, Equipment, and Natural Resources --Long-Lived Assets, Components of Asset Cost, Valuing Assets, Depreciation of Assets, Impairment of Assets, Disposal of Assets, Depletion of Assets, Natural Resources, Reporting and Analyzing AssetsControlling and Reporting of Intangible Assets --Intangible Assets, Types of Intangible Assets, Intangible Asset Impairment, Research & Development Cost, Reporting and Analyzing IntangiblesValuation and Reporting of Investments in Other Corporations -- Approaches to Investment Accounting, Debt Held to Maturity, Debt for Sale, Holding Less than 20% of Shares, Holding 20-50% of Shares, Ownership: Holding More than 50% of SharesReporting of Current & Contingent Liabilities -- Liabilities, Current Liabilities, Contingencies, Reporting and Analyzing Current LiabilitiesThe Time Value of Money -- the Time Value of Money, Future Value, Single Amount, Annuities, Additional Detail on Present and Future Values, Yield, Valuing Multiple Cash Flows, Present Value, Single AmountReporting of Long-Term Liabilities -- Overview of Bonds, Valuing Bonds, Bond Retirement, Reporting and Analyzing Long-Term LiabilitiesReporting of Stockholders' Equity -- Understanding the Corporation, Stock Transactions, Rules and Rights of Common and Preferred Stock, Additional Detail on Preferred Stock, Dividend Policy, Cash Dividend Alternatives, Reporting and Analyzing Equity, Additional Topics in Stockholders' EquityDetailed Review of the Income StatementDetailed Review of the Statement of Cash Flows Special Topics in Accounting: Income Taxes, Pensions, Leases, Errors, and DisclosuresAnalyzing Financial Statements'
'Thinking Skills are some of the most valuable skills you can learn today. The reason is simple. While in the past, people...
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'Thinking Skills are some of the most valuable skills you can learn today. The reason is simple. While in the past, people went to work for their manual skills, today they go to work for their mental skills. We live in an Information Age, no longer an Industrial Age. That's why brain has replaced brawn, and strength in thinking has replaced strength in muscles. No matter what kind of business you work for, nor what kind of job you do, today you are expected to apply a range of thinking skills to the work you carry out. This includes using your judgment; collecting, using, and analyzing information; working with others to solve problems; making decisions on behalf of others; contributing to ideas to innovate and change; and being creative about how your job can function better.This book covers all of these skills. It will show you that, whatever you think about your mental abilities or the level of your IQ or your formal education, your brain is the most powerful organ you possess. It is the tool that, if used skillfully, can help you perform better in your job, better in your team and better in your organization. By developing your thinking skills to meet the needs of the modern world, you are guaranteed to succeed.'
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Major Algebra II Themes
There are certain things that we see pop up time and time again in Algebra II. It's important to notice that there are certain types of graphs that will be mentioned more than once. These themes include graphs, functions, equations, and new notation.
We've met them all before, but we were just acquaintances back then. Sure, we'd wave "hello" to them in the hallway, but we never really got to get to really know them. This time around, we'll approach these themes from all sorts of angles. Not only that, but we'll start to learn about how they're all related to each other.
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Users toss a virtual coin or die to investigate the law of averages. The outcomes of multiple experiments (consisting of 10000 tosses each) can be graphed on the same plot to facilitate visualization of trends. An activity is provided to facilitate thinking about the law of averages with the applet.
This applet performs traditional elementary row operations keeping track of the entire process. It also allows fraction, integer, or decimal entries and preserves these types throughout the row reduction process.
This applet allows the user to see regions of integration for double integrals in rectangular or polar coordinates. The applet uses classes from the article "Flash Tools for Developers: Parametric Curves on the Plane."
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0321744446Hardcover New 0321744446Blitzer continues to raise the bar with his engaging applications developed to motivate readers from diverse majors and backgrounds. Thinking Mathematically, Fifth Edition, draws from the author's unique background in art, psychology, and math to present math in the context of real-world applications. The author understands the needs of nervous readers and provides helpful tools in every chapter to help them master the material. Voice balloons are strategically placed throughout the book, showing what an instructor would say when leading a student through a problem. Study tips, chapter review grids, Chapter Tests, and abundant exercises provide ample review and practice.
Editorial Reviews
Booknews
An anthology of fiction, poetry, history, literary criticism and folklore about the mountainous region and the influences on it. The selections in volume 2 are organized around themes such as family and community, dialect and language, sports and play, and regional identity and the future. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Meet the Author
Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob's love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Thinking Mathematically, Bob has written textbooks covering introductory algebra, college algebra, algebra and trigonometry, and precalculus, all published by Prentice Hall. When not secluded in his Northern California writer's cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roost
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Follow Us
About the NVC Math Department
About the Mathematics Department
The Northwest Vista Math Department strives to educate its students and help them see the value of mathematics as an integrated discipline both in academics and in the real world.
___________________________________________________________
Math Mission
Our mission is to help students do the following:
1) Appreciate the relevance
of mathematics, its relationship to other disciplines, and its role,
both in society and in their personal lives.
2) Develop the attitude,
skills, and knowledge necessary to understand, analyze, and solve
practical problems, with a special emphasis on critical-thinking and the
application of mathematical techniques.
3) Understand the benefits of
cooperative learning and how it can be balanced with independent
learning to foster lifelong learning.
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Math Survival Guide Tips and Tricks for Science Students
9780471270546
ISBN:
0471270547
Edition: 2 Pub Date: 2003 Publisher: Wiley & Sons, Incorporated, John
Summary: This second edition of 'Math Survival Guide' provides tips for science students in the form of a quick reference/update guide. It uses an approachable tone and appropriate level and includes good problem sets.
Appling, Jeffrey R. is the author of Math Survival Guide Tips and Tricks for Science Students, published 2003 under ISBN 9780471270546 and 0471270547. Three hundred five Math Survival Guide Tips and Tr...icks for Science Students textbooks are available for sale on ValoreBooks.com, one hundred fifty five used from the cheapest price of $6.06, or buy new starting at $38.95
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A web hosted courseware of undergraduate single and many-variable calculus for physics and engineering students, with...
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A web hosted courseware of undergraduate single and many-variable calculus for physics and engineering students, with animated and interactive graphics. It is based on a course "Mathematical Introduction for Physicists" of the Tel-Aviv University.In addition to text, examples and exercises, the courseware takes advantage of modern technology with interactive and animated graphics (over 110) that can be projected in class, and accessed at any time by the students.Math Animated is technically based on SVG and MathML - open standards, developed by the Web Consortium, without the need of proprietary software. It runs on the most popular platforms: Windows, Mac and Linux.About 10% of the material, including text and graphics is open and does not require any registration.
| 677.169 | 1 |
The program is designed to prepare students for graduate study or a career in a mathematical field. The program offers a more traditional track in pure mathematics as well as an applied math alternative track. As such, the program conforms to the guidelines of the Mathematical Association of America, and in addition gives students material and tools of theory, abstraction and inquiry that would be useful in a graduate mathematics program.
Learning Goals:
Students will explain how they know mathematical truths, and prove some of the basic ones.
Students will express mathematical ideas verbally and in writing.
Students will identify major mathematicians and explain and critique the major ideas of mathematics.
Students will apply problem-solving techniques to problems they have never seen before.
Students will be familiar with the application of technology in mathematics.
Assessment Criteria:
Students will identify the properties and graphs of the elementary functions: that is, polynomials, rational functions, exponential functions, logarithms, trigonometric functions and their inverses, and hyperbolic functions.
Students will differentiate combinations of elementary functions, including functions of several variables. Students will be able to apply all of the basic integration techniques.
Students will perform what might be thought of as the core skills of linear algebra: in particular, matrix and vector calculations, for instance, determination of whether a set of vectors is linearly independent, or mutually orthogonal.
Students will solve problems from probability involving set theory, combinations and permutations, and probability distributions.
Students will use the basic ideas of statistics, including identifying methods for attacking various statistical problems.
Students will use logic and set theory in other areas of mathematics, in particular to understanding and proving statements in abstract algebra and elsewhere.
Students will apply mathematical ideas to problems from other disciplines.
Pure Track – Students will be able to prove mathematical theorems requiring complex arguments.
Applied Track - Students will be able to apply mathematical and/or statistical modeling to a discipline of special emphasis chosen by the student.
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20 Common Mathematics Topics Explained
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The following twenty mathematics topics are discussed in terms of the areas that each might study and the nature of the mathematics involved. As mathematics is a constantly developing and expanding area of study, it is unrealistic to consider that this collection covers every significant area of mathematics and application of mathematics.
It is also less than ideal to list these topics in progressive difficulty as individual talent and interest will make some studies easier for one person than another. However, the hope is that they will develop in understanding and knowledge and that they will provide a guide to the breadth and brilliance of mathematics.
1. Pre-Algebra
In preparation for a study of Algebra, it is important to have a solid grounding in concepts and applications that will provide the basis for further study. This includes a range of relatively simple concepts and conventions including, Absolute Value, Base Number System, Fractions and the Real Numbers.
Our first experience of Mathematics is usually through Arithmetic, but that's not to say that they are synonymous. In fact, the ability to perform arithmetic has little bearing on the ability to understand and apply mathematical concepts. It is handy and certainly speeds up the process, but there are numerous examples of brilliant mathematicians and scientists that struggled with Arithmetic.
Arithmetic is largely centered on the ability to use the basic operations of addition, subtraction, multiplication and division. Much of this is done through memory rather than a process, but as the numbers become larger, most of us need to revert to pencil and paper or at least taking time to think through the task.
Furthermore, the place of Arithmetic Laws, such as the Commutative Law, Associative Law and Distributive Law, plays a significant role in developing an understanding of processes including factorization and simple algebraic operations.
Similarly, a working knowledge of the Cartesian Plane is essential to further study. The Cartesian Plane is formed by the intersection of two axes, the horizontal labeled "x" and the vertical labeled "y". The point of intersection is called the origin and has a value of zero on each axis. From the origin the axis are graduated with positive numbers to the right and up and negative numbers to the left and down.
Points on the plane are located at the intersection of grid lines drawn from each axis. The point (2,3) is found vertically in line with the number 2 on the x-axis and horizontally in line with the number 3 on the y-axis.
This is the basis for visual representation of functions, vectors and the manipulation of figures through transformations.
Within a Pre-Algebra study there should also be a reference to the investigation of Pythagoras Theorem. Pythagoras Theorem works through the agency of right angle triangles. To apply it fully, we need to identify that the side opposite the right angle, the longest side, is the hypotenuse. With this understood the Theorem states that the sum of the squares of the two shorter sides will equal the square of the hypotenuse.
By manipulating the Theorem, it is possible to determine the value of the third side of the triangle when provided with any two other sides. When given the hypotenuse and one other side the Theorem can become:
c2 – a2 = b2
Within the study of Pythagoras Theorem, a number of triads can be found. These include, (3,4,5), (5,12,13) and (7,24,25) and they are sets of side lengths that will always form a right angle triangle. Even when they are increased by scale factors, they maintain their form, such as, (6, 8, and 10) and (15, 36, 39).
2. Algebra
Mathematics is basically about recognizing patterns. To represent these patterns and the ideas that grow from them a system of numbers, pronumerals and conventions was devised, which is known commonly as Algebra.
This includes applications that focus on functions of degrees greater than one. The degree of a function is determined by the highest index of a variable in the function. For example, a quadratic function is a second degree function as it is expressed as f(x) = ax2 + bx + c. The exploration of these functions includes their factorization into roots.
Algebra also addresses the concepts and conventions of Set Theory. These investigate the principles of universality – all possible events, subset – sets within sets, intersection and union.
Other relevant concepts include infinity and the places geometric and arithmetic mean can play in modeling real-life events.
3. Geometry
Geometry is the study of shapes, angles and where things really are in relation to other things. When a two-year-old is working out which block goes through which hole in the shape bucket, they have begun the study of geometry.
Through a process of tests and definitions, we are then able to identify and classify the variety of shapes through the lengths of their sides and the angles of their vertices. Such investigation leads us to recognize patterns in the angles that lines make when they intersect and how we can apply these in areas such as architecture, navigation and art.
Geometry also provides a means for discussing spatial awareness. The use of direction and distance allows us to locate items and, more importantly, it allows us to discuss their position and movement in an explicit and measurable way.
The study of transformations allows us to discuss other movements of objects as well, including reflection and rotation. We can also distinguish changes in shape through dilation, that is, enlargement or reduction.
Geometry can be as concrete as the square peg having to go into the square hole or as abstract as an imaginary plane where objects are manipulated through space and time.
Within the study of Space, a major element is the topic of Polygons. A Polygon is a two-dimensional closed figure consisting of straight lines only. Traditionally we think of hexagons, pentagons and even squares as Polygons, but the definition allows for more.
The neat evenly drawn shapes that are often examples of Polygons are actually regular Polygons. These are shapes with the same length sides and the same size angles. However, irregular Polygons are very common in real-world applications.
Beyond the concrete examples of Geometry, there is also a theoretical, more abstract, approach that allows for the study of hypercubes and hyperplanes, where traditionally geometric figures are given the scope to grow beyond their traditional dimensional conventions.
4. Trigonometry
Trigonometry works from the relationships between the sides of a right-angle triangle.
The side of the triangle that isn't connected to the right angle is called the Hypotenuse. This is the longest side of the triangle.
With that in mind, decide which vertex, corner, you are looking from. This is your orientation.
The side of the triangle that joins this vertex is called the Adjacent side.
The side that doesn't join this vertex is called the Opposite side.
Once these sides are identified, they can be used to find unknown lengths and angles of the triangle. This is because, regardless of the length of each side, the ratio of the side lengths will always be the same for a given angle.
For example, if the vertex forms a 30° then the ratio of the Opposite side and the Hypotenuse will always be 1:2. Whether the sides are 3 and 6 inches, respectively, or 300 and 600 miles, at that angle the ratio will always be the same. Using the principles of Similar Triangles these properties can be applied to any size right-angle triangle.
The origin of the values attributed to each relationship is founded on the construction of a Unit Circle, that is, a circle with a radius of 1 and is centered on the origin of a Cartesian plane. As this radius is rotated around the circle, its height above the x-axis can be read as the y-coordinate and in the Sine relationship this draws the y-coordinate into ratio with the hypotenuse, the radius, of 1.
Similarly, the horizontal distance from the origin to the intersecting point of the circumference of the unit circle and the radius is the x-coordinate. This value placed in relationship with the radius, 1, gives the Cosine value.
The same values are also able to be used to determine the Tangent relationship.
Further application of the geometric properties of circles and triangles allows for greater exploration of Double and Half-Angle formulae and Addition formulae.
5. Pre-Calculus
In preparation for the study of Calculus, there a number of elementary concepts and operations that must be understood. These provide the basis of calculations and descriptions and allow for creative and comprehensive discussions of Calculus.
Among these are Transformations of objects in space, including, Translation, Rotation and Reflection, and the use of coordinate systems other than the Cartesian, such as Polar and Spherical Coordinates. Matrix operation including the use of the Determinant, Scalar Matrices and Rotation Matrices are also important.
Furthermore, the ability to use and manipulate complex numbers, exponents and logarithms should be studied and placed in the context of functions. Exploration should look further at the way these functions are handled in calculus, as well as investigating their representation through the study of Conic Sections.
Conic Sections are the shapes created by taking cross-sections at varying angles through a solid cone. They include parabolas, through a vertical cross-section, ellipses, through an angled cross-section, and circles, through a horizontal cross-section.
6. Calculus
Investigations into the gradient, or slope, of a graph are often drawn to the change in one variable in relation to the change in another. The subsequent discussion on the rate of change can far-reaching implications and the Mathematics behind it has a variety of applications. When such investigations move from the confines of straight line graphs to include the gradient of curves, then we enter the study of Calculus.
To determine the gradient of a curve, an approximation can be made. Using the same principle of change in one variable being placed in ratio to the change in the other, a rough idea can be gained. In order to improve the accuracy, the approximation is reduced to smaller and smaller intervals until they reach a limit that is infinitely close to, but not equal to, zero. At its smallest possible interval, the gradient is virtually a tangent to the curve, that is, a line that touches only at one point.
Being able to determine the gradient of a curve at any given point means that we are able to find the points at which the curve reaches its maximum value, minimum value or pauses, inflection points, in its progression.
The use of Calculus to model real-world motion allows us to discuss a range of "rate-of-change" scenarios. This makes it applicable in area from fluid dynamics to nanotechnology and has even been used to maximize investment portfolios.
The derivative of a formula provides us with the equation of the gradient to the curve. In its most simple form this is done by multiplying each term by the degree of the index of its pronumeral and reducing that index by 1.
If we allow this equation to equal 0, we can then determine the x-value of the turning point of the curve:
= 2x + 2
x = -1
Substituting this value back into the original equation provides us with the y-value:
Y = (-1)2 + 2(-1) + 1
= 1 – 2 + 1
= 0
The turning point for this curve is at (-1, 0).
More sophisticated curves and applications require more complex differentiation, but the use of Calculus to help map and model mathematical ideas is invaluable.
7. The History of Mathematics
In the words of Marcus Garvey, "A people without the knowledge of their past history, origin and culture is like a tree without roots." While it may seem that a study of the History of Mathematics would be better suited to a Humanities program, it must be understood that such a study is deeply relevant to the understanding and future of mathematical study.
Whether it is to study the profound contributions of the Pythagoreans or to investigate the formalization of areas such Topology, the process and influences that encouraged and engendered the development of mathematics can inspire modern thinkers. Even exploring the social and political influences that brought about great advances can have a bearing on the directions and progress of mathematics today.
The origin of calculus may seem an insignificant topic against the continuing development and innovations associated with it, but the reality of the its power to describe the motion of planets holds profound significance. In the same regard, the advancement of algebra from simple roots to become the language of mathematics is fundamental to the creation of new system and understandings.
The study of history has benefits in all areas of endeavor. Perhaps it is even more relevant in the study of mathematics than most other spheres of pursuit.
8. Number Theory
The study of numbers as integers, fractions and groupings defined by their properties is a delving into the nature of the building blocks of mathematics. Scientifically, numbers can be classified and studied for their properties, similarities and individual features.
Concepts, such as prime numbers, perfect numbers and transcendental numbers, provide a structure for the continuing study of numbers beyond, real, rational and complex. This can include the development of theorems around the use and manipulation of these numbers, such as the Prime Number Theorem and the Prime Factorization Algorithm.
The study of Number Theory calls on a knowledge of concepts such as congruency and convergence, so as to discuss the characteristics of numbers and the functions through which they operate.
9. Finite Mathematics
The study of Finite Mathematics is relevant to students of psychology and sociology. Largely it is focussed on the theory of probability and matrices.
Probability furnishes the mathematical foundations for statistics. Although this is a theoretical area of mathematics, the applications used in the study of Finite Mathematics make it a more real-world specific topic. This extends into the investigation of union and intersection, while also considering mutually exclusive and disjoint events.
The use of matrices to assist in the exploration of probability includes knowledge of matrix multiplication and the applications. It also introduces the use of matrices for linear systems and the properties of inverse matrices.
These two areas of mathematics come together in the study of Finite Mathematics creating a practical and successful form of mathematics for studies that have specific needs.
10. Theory of Computation
The place of devices, mechanical and electronic, to aid calculation in mathematics is an ever developing and expanding field. Similarly, the use of software, ranging from spreadsheets to more sophisticated calculation programs, is constantly undergoing innovation and evolution.
This is probably ideally illustrated by the annual "Record-breaking" effort of university students somewhere in the world setting some poor computer to work to generate π to ten million more decimal places than the students of the year before. One can only imagine the computer sighing loudly and remarking, "If I have to" as it hacks out another list of non-recurring decimals like a cat bringing up a hairball.
Thankfully, there are multitudes of more constructive and purposeful applications of computation devices and principles than this. Whether through rudimentary processes or through the use of Cellular Automaton or the Turing Machine, the study of the Theory of Computation invites and encourages endeavors to improve our understanding of the nature of computational operations.
11. Topology
At the foundation of Topology is the concept of congruency. That is, the ability to say that a shape, argument or set of elements is identical in all ways to another. In Topology, two objects are considered the same if they can be distorted to be congruent without causing change to the properties of each. Although the basis of this branch of Mathematics had been discussed and developed for centuries, the title Topology only became the over-arching name for it near the end of the nineteenth century.
In fact, the study of Topology is often described as an investigations of the properties of an object that remain sound despite the distortion, twisting and stretching of the object. In this regard the discussion of manifolds, knots and dimensions can be held with a recognition that the fundamental topological aspects will be preserved.
Through the study of Topology and the manipulation of objects and shapes, the Mobius Strip can be formed and defined successfully. Similarly, the projective plane and the projective space, both of which involve the intersection of a set of lines through the origin are able to be discussed and explored.
Set-point Topology is more abstract and presents possibilities for further investigations into concepts such as continuity, dimension, compactness and connectedness. With these ideas in mind, the Topological Space becomes recognizable as a set with a collection of subsets that satisfy the definitions of the set.
12. Linear Algebra
Moving beyond the high school understanding of linearity being related to y = mx + c, the study of Linear Algebra invites the use of vectors, scalars and matrices to address the systems of linear functions and their transformations.
This includes the defining and application of vector spaces and the use of vector addition and scalar multiplication. Vectors are largely lines with magnitude, size, and direction. In areas such as Physics, this translates to speed and direction, producing velocity vectors. Using the fundamental operations of addition and subtraction, these vectors can be used to solve problems including exercises in the study forces.
Scalars are effectively real numbers used in the study of Linear Algebra. They can be used to multiply vectors and create new vectors within the same finite vector space.
The use of matrices as a means of representing linear transformations provides a unique representation of the transformation. Using methods of addition, subtraction and multiplication, both scalar and matrix, matrices provide a purposeful and skillful method for manipulating and problem solving in Linear Algebra.
13. Probability and Statistics
According to Benjamin Disraeli, a 19th Century Prime Minister of Britain, there are "Lies, Damned Lies and Statistics". This is a fair assessment of the use of statistics and how they can be manipulated, but the mathematics of statistics is far less malleable.
Statistics is an area of mathematics that organizes information, commonly called data, and uses these structures to study trends. Most people will recognize terms such as average and range and these present the first ideas of "Where most of the data lies" and "How wide the data is spread".
However, it takes only a brief consideration of the data to see that there are different types of average that we can discuss. The three most common are the:
Mean = Sum of the data / The Number of pieces of data (This is also called the Number of the data)
Mode = The most frequently occurring response.
Median = The middle number when all the data is organized from lowest to highest.
The Range of the data is the difference between the highest and lowest value of the data.
The trick to reading statistics is to look as closely at what is not being highlighted as you do at what you are being directed towards. Celebrating the success of two thirds of the class passing a test, may avoid the fact that three quarters of the class didn't score more than 60%.
More sophisticated applications of statistics include the deriving of standard deviation and the construction of normal distribution, uniform distribution and binomial distribution. From this work, further study into poisson distribution and covariance follow as a natural progression.
Statistics are great for making a case, but need to be handled with care.
One of the most contentious areas of Mathematics is Probabilities. This largely due to the fact that the results of the theoretical calculations of Probabilities are so readily shown as inaccurate. The topic often loses credibility, its proponents lose faith in the early stages and it can take a significant amount of explanation and goodwill to pull it back into the realm of "real" mathematics.
The central rule to Probabilities is the number of favorable outcomes divided by the number of possible outcomes. In this context favorable doesn't always mean that the outcome is pleasant or good, it simply means that it is the one being sought. No-one considers an earthquake favorable, but if you're determining the probability of an earthquake occurring then the data supporting the event is treated as the "favorable outcome".
More complex Probability calculations are the result of events being dependent on each other and combinations of events occurring that have no determining connection, often described as Mutually Exclusive and Conditional Probability.
14. Discrete Mathematics
The distinction between Discrete and Continuous data is important in terms of the processes and operations that can be applied. By definition, Discrete data is that which can only be discussed in whole or specific units, while continuous has the capacity to be graduate along a number line.
As examples, the number of students in a class must always be treated as Discrete data, that is you can't have half a student. Whereas the height of the students can, if the measuring apparatus is capable, be taken to such extent that it may consist of numerous decimal places.
So, when we start to discuss Discrete Mathematics we are talking in terms of units that must stand separate from each other. Through this limitation on the values to be used, the study of algorithms, logic and binary systems can be introduced and explored.
Binary systems are limited to working with a base of 2, that is, they have only two numbers 0 and 1. Using this structure, numbers are expressed in terms 0 and 1, for example, 2 is 10. That is, 0 is 0, 1 is 1, but instead of going to a third number, the system now moves into double digits, so 2 becomes 10.
It may be worth noting that, as binary system in base 2, powers of two become comparable powers of "ten".
The restriction of data to Discrete forms also makes it possible to investigate areas of Combinatory, that is, the study of Permutations and Combinations. This allows us to investigate the structure and possibilities of a range of outcomes. While both are focused on the grouping of elements, the distinction between them is found in the understanding that for Permutations the order of the elements is important, while for Combinations it is not.
Calculations of Permutations and Combinations rely on the Factorial function. Indicated by the inclusion of an exclamation mark after the number, the Factorial of a number is the product of all numbers below it to 1. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
When calculating the Permutations of "r" elements selected from a set of "n" possible items the first thing to consider is whether or not repetition is allowed. If it is the answer is nr, that is, n x n x n … r times.
However, if repetitions are not allowed, then the number of possible items decreases with each selection. So the answer will be n x (n-1) x (n-2) … r times. This is best illustrated as n!. But to stop the process after r terms, we must also divide by the terms after r.
As an example of this consider a group of twelve students from which only three are to be chosen. The possible Permutations are given by:
When addressing Combinations the removal of the constraint of order calls for additional calculations. Largely this means reducing the formula by how many ways the objects could be ordered, so the rule for determining the Combinations possible of "r" elements selected from a set of "n" possible items without repetition is:
n!
-------
r!(n-r)!
In the course of such a study, aspects of Fibonacci's Sequence, Pascal's Triangle and Magic Squares can be explored within the context of Discrete Mathematics.
15. Graph Theory
The area of Mathematics called Graph Theory is a significant and expansive aspect of the study of Space. It includes tangible and real-world elements, while also being rich with abstract and imaginative ideas. Although the basis of this branch of Mathematics had been discussed and developed for centuries, the first published work on the topic was only written in 1736.
This was in response to Euler's "Seven Bridges of Königsberg". The bridges connected two islands in the Pregel River with each other and the mainland. Euler set a challenge to discover a path that crossed all bridges only once. To simplify the problem, Euler created a topological map of the river, islands and bridges. While the map was far from an exact scale drawing of the problem, it contained all the necessary and meaningful information.
Through this exercise, Euler created the idea of Graph Theory to model real-world situations. This included, and has extended, to define the dots and lines of a diagram as vertices and edges. Other concepts were then able to be classified and discussed, such as the degree of a vertex, the number of edges attached to it, a path, the course taken connecting vertices, and a cycle, a path that ends where it began.
Graph Theory has virtually nothing to do with the display of data on a chart and graph paper has little special purpose in the study of Graph Theory. This is because Graph Theory holds a greater potential to explore the abstract and the creative side of pure mathematics.
16. Abstract Algebra
The more that we delve into the structures and nature of Algebra, the further we can move into the theoretical aspects. This is not to suggest that Abstract Algebra lacks a practical context, rather the abstraction of the ideas actually makes it more inclusive of a range of creative and diverse application.
This is evident in the exploration of a range of Algebras, including Boolean Algebra and Lie Algebra. These use the fundamentals of Algebra combined with principles of logic and additional conditions.
Abstract Algebra can also take into account the study of Group Theory. Through Group Theory we can investigate laws such as the Associative Law – a + (b + c) = (a + b) + c, the Identity property – a x 1 = a and the Inverse Law – a = √a2 . It can also present ideas regarding a variety of forms of Groups including Abelian, Cyclic, Finite and Sub Groups.
17. Calculus and Convergence
Building on the understanding and competencies attained in Calculus, a more advanced calculus program would discuss further rules for the application of calculus. These could include the Chain Rule, by which a function can be differentiated using an intermediary function, the Quotient Rule, through which functions in a fractional or divisor state can be differentiated, and the Product Rule, through which functions being multiplied together can be differentiated.
The concepts of Convergence and Divergence are necessary to the continuing study of calculus. By applying Radius of Convergence as a test, it is possible to verify that a function is indeed converging.
The divergence of a function, that is, its continuing growth toward infinity or its oscillating nature that limits its ability to converge, can be tested by using the Integral Test.
The application and study of series including Taylor Series, Power Series, Maclaurin Series and Harmonic Series is able to be carried out in terms of convergence and practical use.
Other practical applications, such as determining Arc Length and the Surface of Revolution would also be extensions on the fundamental understanding of Calculus.
18. Differential Equations
The study of Differential Equations is an introduction to the application and purpose of calculus in the mathematics. Through the exploration of derivatives, both ordinary and partial, the uses of the Differential Equations can be placed in practical and real-world scenarios.
Differential Equations contain derivatives and the process of solving them involves integration, but can also use the separation of variables method. The resulting equation will usually be of a form y = … or f(x) = … .
Through investigation of Differential Equations, methods of solving physical problems including the Fourier and Laplace transformations and Bessel Functions are explored. These solutions can involve first and second order differential equations.
The order of a Differential Equation is determined by the level of derivatives present. The highest level of highest derivative in the Differential Equation, for example, a second order Differential Equation will have at least one second derivative; it may also include first derivatives and constants.
19. Differential Geometry
The study of Differential Geometry is often seen as a study of curvature and distances, on surfaces. This can also be seen as development from the work on Surface of Revolution in Calculus.
Through Differential Geometry it is possible to investigate concepts like the Mean Curvature of a surface and the Gaussian Curvature. These study the amount of bend in a surface and curvature as a property of space.
In dealing with curvature, there is also scope to investigate the properties and characteristics of tangents. This reflects the initial intent of Calculus to define the gradient of a curve and can be extended into the development of Tangent Bundles, which are constructed from the tangent spaces of a series of points.
The use of scalars and vectors plays a role in this work as does that of matrices to represent them.
20. Analysis
Analysis is the study of functions, real and continuous, so as to determine their features and characteristics. This can include the study of Delta Functions, Gamma Functions and Functional Analysis, which allows for the investigation of infinity vector spaces.
From generalized applications of Calculus to determine curves and stationary points, Analysis considers the use overlap of functions through Convolution and the use of measures to assist in the understanding of integration and differential equations. This can include the study of the Lebesgue Measure and the Cantor Set.
Through Analysis there is also study of Bernoulli Number and the Fourier Series. Through these the study of trigonometric functions is further explored within the realm of calculus and through the operations of Bernoulli's Number and the Fourier Series.
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Amy Sue Miller -
May 31, 2012 at 11:39 pm
Serial killers are just like everybody else when they're not murdering innocent people. They have to work for a living. Even a bloodthirsty maniac needs to put food on the table and pay the rent or the mortgage.
Rumors can be one of the most destructive forces on the face of the earth. Every day, people's lives, careers, businesses, and futures are destroyed by rumors. Not even the rich and powerful are safe from rumors.
Most of the infamous barbarian raids took place during what is called Europe's 'Migration Period,' which took place over a 400 year span, beginning around 390 AD. Groups such as the Goths, Franks, Suebi, Vandals
For years, people have studied the numbers used throughout the Bible to gain an understanding of the significance of particular numbers. Some people believe that the importance of numbers can then be applied to our lives.
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Introduction to Discrete Mathematics with ISETL - 96 edition
Summary: Intended for first- or second-year undergraduates, this introduction to discrete mathematics covers the usual topics of such a course, but applies constructivist principles that promote - indeed, require - active participation by the student. Working with the programming language ISETL, whose syntax is close to that of standard mathematical language, the student constructs the concepts in her or his mind as a result of constructing them on the computer in the syntax of ISETL. This dr...show moreamatically different approach allows students to attempt to discover concepts in a ''Socratic'' dialog with the computer. The discussion avoids the formal ''definition-theorem'' approach and promotes active involvement by the reader by its questioning style. An instructor using this text can expect a lively class whose students develop a deep conceptual understanding rather than simply manipulative skills. Topics covered in this book include: the propositional calculus, operations on sets, basic counting methods, predicate calculus, relations, graphs, functions, and mathematical induction. ...show less
Edition/Copyright:96 Cover: Hardcover Publisher:Springer-Verlag New York Published: 09/19/1996 International: No
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David Lippman Melonie Rasmussen
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2009 AMATYC Conference
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Editorial Reviews
VOYA
Designed to appeal specifically to a young teen audience, the Math Success series might be useful for reviewing math skills but will not, most likely, help readers pick up these skills on their own, as suggested in the authors' introduction. The short format and many examples give these titles an accessible look. Each titled section takes up exactly one spread, making it easy to find a topic by browsing the table of contents or even just flipping through but not always allowing enough space for the best explanation. Small black-and-white graphics of teens making encouraging remarks appear every other page or so. A gray bar across the bottom of each page provides space for definitions—many of which, unfortunately, should have appeared in the body of the text—and suggestions for fun ways to practice skills or other comments that seem intended only to fill the space: "Calendars measure long periods of time. Clocks measure short periods of time." Although written in a straightforward manner, the brief text leaves out much and might only further confuse struggling students. Some terms such as "place value" are introduced into the text without any definition or explanation. The term "regrouping" is used in place of "carrying" and "borrowing" and is never explained adequately. Many of the short explanations, although not technically wrong, might be misleading in their brevity: "the denominator... tells you the total number of parts there are," or "Variables... are used in mathematical expressions to stand for names." Both books in the series suffer from a lack of continuity. After the assertion that addition and subtraction are inverse operations, explanations are found inseparate chapters that repeat much information without cross-references. Skills are not linked or related in an obvious manner, and there is no overriding explanatory narrative to describe such concepts as place value, inverse operations, estimation, or variables are actually intended to clarify. Students might be drawn to these books for their format and might find them useful to brush up on skills. To expand their understanding of mathematics truly, students will need someone by their side to explain concepts to them and probably will find these titles more trouble than they are worth. Index. Illus. Further Reading. VOYA CODES: 2Q 4P M J (Better editing or work by the author might have warranted a 3Q; Broad general YA appeal; Middle School, defined as grades 6 to 8; Junior High, defined as grades 7 to 9). 2000, Enslow, 64p. PLB . Ages 12 to 15. Reviewer: Nina Lindsay SOURCE: VOYA, June 2001 (Vol. 24, No. 2
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When you use the Prentice Hall Mathematics program, you have four options: Course 1, 2 and 3, and Algebra Readiness. The final installment will round out your child's pre-Algebra knowledge, when needed, provide a smooth transition between Courses and help him or her fully grasp the subject. The curriculum for homeschooling covers algebraic expressions and integers, linear functions, one-step equations and inequalities, and area and volume.
Prentice Hall Mathematics: Algebra Readiness is designed to help your child ease into the next level of Algebra. First, you'll introduce the concept, which your child can follow along with using Math problems. Next your child will have to apply the new ideas he or she has learned. Finally, your child will use the information beyond simple problem solving, tackling accelerated Math concepts.
This program is designed to help your child focus on these key areas:
Use algebra concepts to solve complex word problems.
Recognize and understand square root and root symbols.
Explain why a certain equation is the correct one to solve a problem.
Use proper equations to solve real-world problems.
Calculate area and volume of a shape.
Using the materials in Prentice Hall Mathematics: Algebra Readiness, you'll be able to guide your child through the curriculum. The problems included in the program keep your child engaged and learning, and the teacher materials keep you up to date on your lessons. For more information on the materials included in Prentice Hall Mathematics: Algebra Readiness, visit the Features and Benefits
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This website is a project by Marc Renault, supported by Shippensburg University. The goal is to make a complete library of...
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This website is a project by Marc Renault, supported by Shippensburg University. The goal is to make a complete library of Geogebra applets for Calculus I that are suitable for in-class demonstrations and/or student exploration.
This is a collection of 339 videos that work out typical exercises that first, second and third semester calculus students...
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This is a collection of 339 videos that work out typical exercises that first, second and third semester calculus students are asked to solve. The lengths of the videos range from a couple of minutes to up to seven minute depending on the complexity of the exercise. They are all closed captioned, and graphs and other diagrams accompany the words and equations when applicable.
The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts,...
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The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and "play" with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly "see" how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.
Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math...
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Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math (basic arithmetic and math to calculus), statistics, biology, physics, chemistry, finance, and other topics. The topics cover K-12 levels and higher education. The simple and clear presented information enables learners to see and review the topics and how to solve the problems at their pace with as much practice as they wish. In particular there are over a thousand videos just for mathematics. The site also contains a handful of interactive mathematics learning objects that are of the drill and practice type.
This site contains a set of Java applets which can be used in undergraduate mathematics. These applets include regression...
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This site contains a set of Java applets which can be used in undergraduate mathematics. These applets include regression applets, 2D graphing applets, applets to illustrate linear, quadratic, exponential and trigonometric functions, Riemann sums applets, and a Java MathPad, which can be used as a limited CAS which allows the user to define its own functions, evaluate them at any point, perform symbolic and numerical differentiation and limited symbolic integration. These applets all use a common interface and syntax. There is an nextensive help system to guide the user.
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In PDF format, essays include "The Role of Hand-Held Computer Symbolic Algebra in Mathematics Education in the Twenty-First Century: A Call for Action!"; "The Role of Graphing Calculators in Mathematics Reform"; "The Evolution of Instructional Use of Hand Held Technology. What we wanted? What we got!"; "Reform Backlash - How do we deal with it?"; and "A Computer for ALL Students - Revisited" from The Mathematics Teacher.
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Introduction to Excel Part Two: Formatting an Existing. Spreadsheet. Purpose.
Upon completion of this tutorial you will have learned how to format the following:
.Edexcel AS/A level Mathematics Formulae List – Issue 1- September 2009. 3. The formulae in this booklet have been arranged according to the unit in which ...
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Graph This
In my last article I explored the idea of using calculators for teaching
elementary-school mathematics and concluded that calculators are not
useful for teaching arithmetic.
What about higher mathematics, such as algebra, trigonometry, and
calculus? More and more high-school math courses, even math programs
widely used by homeschoolers, include or require the use of graphing
calculators.
Why is this? Certainly, there must be a good reason why all these
curriculum writers think it is worthwhile to include the use of a
graphing calculator in their courses.
From the teacher's point of view, there is a certain amount of
"technoglam" associated with having a high-tech curriculum.
From the calculator manufacturer's point of view, including
calculators in every major math curriculum is a very financially
desirable goal. Texas Instruments sold its 40 millionth graphing
calculator in 2006. At $150–$200 apiece, that comes to multiple
billions, and that doesn't include the billions earned by Casio,
Hewlett-Packard, and the other manufacturers.
Can You Learn Higher Math Without a Graphing Calculator?
This question really doesn't need to be asked. Most of the higher
math taught is colleges was formulated long before the invention of the
pocket calculator. Most mathematics doesn't require a calculator
and many mathematicians detest having to use either a calculator or a
computer for anything.
To a mathematician, finding a proven method to get the answer and an
exact mathematical expression for the answer is enough—you
don't need to compute the decimal value of the answer to 10
decimal places.
For example, the equation:
x2 + 2x - 2 = 0
has two answers that you can find by mathematically solving the
equation:
-1 + √3 and -1 - √3. Tracing the graph using a graphing calculator you
get an answer around .732 for one of these and around -2.732 for the
other. With judicious playing around with the calculator's scale
and trace functions, you can get answers to higher precision than that.
You will have found the correct numerical solutions to the equation, but
that's not what math is all about.
Math is learning how to solve problems and come up with an exact
expression for the answer. You only compute the decimal approximation of
the answer when the problem requires it.
Does a Graphing Calculator Help You Learn Math?
A number of articles quote the fact that there is a positive correlation
between the number of days per week spent using a graphing calculator
and test scores. This is misleading. Correlations may sound significant,
but that can be deceptive.
First, in this case, the correlation only holds for some countries.
Other countries had the exact opposite result. Also, a corellation
between two things does not mean that one thing causes another. A
positive correlation only means that the two quantities go up together
and go down together. For example, in St. Louis city, there is a
correlation between the amount of ice cream consumed and the number of
murders committed. Do you think eating ice cream causes murder, or the
other way around? No, both are results of the summer heat.
Use of a graphing calculator does not necessarily cause better test
scores. Maybe the greater number of days using a graphing calculator
only means a greater number of days studying mathematics and that is the
cause. Or maybe students who do well in math just like to play with
their calculators and the cause of the good scores is something else
entirely. Don't be fooled by correlations.
You don't need a calculator to learn mathematics. For example, to
learn order of operations in Algebra 1, you learn the mnemonic
"PEMDAS" (parentheses, exponents, multiplication and
division, addition and subtraction). You need to know PEMDAS in order to
accurately use a graphing calculator. The calculator doesn't help
you learn it.
When I am doing problems in statistic, often the writeup for a problem
will take multiple sheets of paper. The part where I use my calculator
is the last line where I actually need to run the numbers. The
calculator did not help me until I reached that point and a scientific
calculator costing less than $20 can take care of the last line.
Graphing calculators actually can hinder math learning in a number of
ways:
The calculator doesn't help you learn to draw and
understand graphs. People who learn by doing—"kinesthetic
learners"—do not benefit from letting a graphing calculator
do it for them.
Graphs on a graphing calculator have no permanence. If you want
to go back and study what you did a week later, a hard copy graph is a
necessity.
You have no way to check your answer on a calculator if you
don't know approximately what answer to expect. If you were inept
at entering a calculation, you will never know. The old computer
expression G.I.G.O. (garbage in, garbage out) applies even more to
calculators.
Calculators lead to passivity and lack of creativity.
Mathematicians should always be thinking, "Can I prove the
validity of this result?" Using calculators, you tend to accept
whatever answer the calculator comes up with.
Use of graphing calculators is causing curriculum to be designed
around the calculators. Time spent learning how to use a graphing
calculator is time not spent learning how to solve math problems the
traditional way. So far, this has already caused high-school calculus
texts to be redesigned, and similar changes have been proposed for
algebra and advanced math.
What is a Graphing Calculator Good For?
As a Math Manipulative. Just like you can use Cuisenaire Rods to help
you conceptualize how to add and subtract, the graphing calculator can
help you discover the shape of various graphs and how the graphs change
when you change the equation. You can illustrate the idea of roots,
continuity, differentials, etc. These concepts can also be illustrated
with diagrams in a book. However, in my experience, I only really
comprehend the important details of the shape of the graph of a function
when I plot the points and connect the dots myself.
For Checking Your Work. A calculator is the fastest way to check the
result of a long computation. It lets the student check himself, saving
time for a harried homeschool teacher.
As a Computational Tool. I do not enjoy unnecessary work, especially
when the product is inferior to what I can get using tools with far less
effort. It's easier to use a rotary saw instead of a hand saw, to
use a calculator instead of pencil and paper, and to use a graphing
calculator with a multi-line display instead of a scientific calculator.
On the other hand, it may be worth it to put up with a little
inconvenience to save the $130 difference in price.
Note also, the more advanced graphing calculators are too powerful. The
data storage capabilities of programmable calculators make it possible
for them to be used to cheat on exams, so many schools forbid their use
in tests. I had to buy a less capable scientific calculator for use on
my tests in college.
As a Substitute for Math Tables. Back in the stone ages before
scientific calculators and graphing calculators, if you wanted to find
sin(23°) you would have to look it up in trigonometric tables. I
don't think anyone even publishes these anymore. All the copies on
Amazon appear to be from out-of-print editions.
To use the table, you would look up the angle in degrees (and in some
editions, minutes, and seconds), in the rightmost column of the table.
Each row contains the angle in radians and the value of the sine, cosine
and tangent of the angle. To get secant, cosecant, and cotangent, you
would have to take the reciprocal of the appropriate function from the
table.
It is much easier to type in an angle, push one button, and read the
result. But for that you don't need a graphing calculator. A
scientific calculator will do the job at a much lower price.
Summing Up
Graphing calculators have their place. . . . but I don't believe
they belong in high school math classes. The calculator distracts too
much from actually learning the mathematics. Also, learning to use a
graphing calculator is not a trivial process. The e-book of instructions
for my TI-86 is 419 pages long.
I would urge you to choose math courses that minimize the overuse of
graphing calculators. BJU's Precalculus text is a good example. It
specifically tells students not to use calculators for most exercises,
and has a separate appendix on graphing calculator use. Then, the summer
before entering college, buy a "For Dummies" book or a
how-to DVD and learn how to use your graphing calculator's many
features
| 677.169 | 1 |
Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd
9780077460396
ISBN:
0077460391
Edition: 8 Pub Date: 2011 Publisher: McGraw-Hill Higher Education
Summary: Be guided through every step of the fundamentals of statistics. It is a great introduction to statistics for college students who have a basic grasp of algebra. It covers all the main concepts effectively and provides a lot of opportunity for practical application. Students are taught problem solving using detailed instructions and examples. It also focuses on the different digital applications used in statistics suc...h as Excel, graphing calculators and MINITAB. It also complements an online course so students can receive more from their course and excellent feedback from the online platform. We offer many top quality used statistics textbooks for college students.
Bluman is the author of Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd, published 2011 under ISBN 9780077460396 and 0077460391. Four hundred eighty Elementary Statistics with CD : A Step by Step Approach with Formula Card and Data Cd textbooks are available for sale on ValoreBooks.com, one hundred eighty eight used from the cheapest price of $29.51, or buy new starting at $139 Does NOT include CD or Formula Card.[less]
DOES NOT include CD or Formula Card. Book only. Ships immediately. USA edition. Used book, good condition with normal wear / markings/writings. Will ship with tracking. Stan [more]
DOES NOT include CD or Formula Card. Book only. Ships immediately. USA edition. Used book, good condition with normal wear / markings/writings. Will ship with tracking. Standard/ Expedited/ Second day Shipping methods available ! Instructor Edition: Same as student edition with additional notes or answers. Has minor wear and/or markings. SKU:9780077460396
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Calculus Demystified - 03 edition
Summary: Here's an innovative shortcut to gaining a more intuitive understanding of both differential and integral calculus. In Calculus Demystified an experienced teacher and author of more than 30 books puts all the math background you need inside and uses practical examples, real data, and a totally different approach to mastering calculus. With Calculus Demystified you ease into the subject one simple step at a time -- at your own speed. A user-friendly, accessible style ...show moreincorporating frequent reviews, assessments, and the actual application of ideas helps you to understand and retain all the important concepts light wear around edges. Some scuffs and scratches. Blacked out price sticker(s) on front...show more/back covers. Cover is bent/creased at corner(s).
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Elementary Statistics
This best-selling text is written for the introductory statistics course and students majoring in any field. Although the use of algebra is minimal, ...Show synopsisThis best-selling text is written for the introductory statistics course and students majoring in any field. Although the use of algebra is minimal, students should have completed at least an elementary algebra course. In many cases, underlying theory is included, but this book does not stress the mathematical rigor more suitable for mathematics majors. Elementary Statistics is appropriate for students pursuing careers in a variety of disciplines. The text emphasizes interpretating data.Hide synopsis
Description:Good. May contain writing and or highlighting. May not contain...Good. May contain writing and or highlighting. May not contain access codes or supplementary material. 2nd day shipping available, ships same or next business day. Get bombed! ! This is the U.S. student edition as pictured unless otherwise stated.
Description:New. LOOSE LEAF! ! WITH CD. STILL IN WRAP. THIS IS A LOOSE LEAF...New. LOOSE LEAF! ! WITH CD. STILL IN WRAP. THIS IS A LOOSE LEAF. This item may not include any CDs, Infotracs, Access cards or other supplementary material.
Description:Very good. 2014. Set includes textbook (ISBN: 013310799X) and...Very good. 2014. Set includes textbook (ISBN: 013310799X) and Math XL for School Student Access Kit. Both are in excellent condition, still wrapped in shrink-wrap. Bottom of plastic has been opened to reveal ISBN. Booksavers receives donated books and recycles them in a variety of ways. Proceeds benefit the work of Mennonite Central Committee (MCC) in the U.S. and around the world.
Description:Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780321836960Looseleaf. New Condition. SKU: 9780321837936-1-0-3 Orders ship...Looseleaf. New Condition. SKU: 97803218379361837936Fine. Hardcover. Almost new condition. SKU: 9780321836960-2-0-3...Fine. Hardcover. Almost new condition. SKU: 9780321836960
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Use a six-column work sheet and a ten-column worksheet to prepare for end of the ... Text: Glencoe Accounting, First-Year Course, Third edition. 2. Glencoe Accounting Chapter ... Technology/Accounting 1 Curriculum 2008.pdf
The materials are organized by chapter and lesson, with one Study Guide and Interventionand Practice worksheet for every lesson in Glencoe Math Connects, Course 2 .
The materials are organized by chapter and lesson, with one Word Problem Practice worksheet for every lesson in Glencoe Math Connects, Course 1 .
The materials are organized by chapter and lesson, with one Skills Practice worksheet for every lesson in Glencoe Math Connects, Course 1. Always keep your workbook handy.
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This biblically-based, homeschool curriculum provides everything needed by both parent and student for an entire year's academic instruction. With the SOS 8th Grade 5-Subject Set, you will receive all five subjects: Bible, History and Geography, Language Arts, Math, and Science. Take a
Students using BJU Press curriculum for 8th grade will cover lessons from the lives of Old Testament characters, a comprehensive survey of American history, and a fascinating look at Space and Earth Science draw your child into a new realm of learning, while Pre-Algebra eases the transition into ...
Discover the fun of homeschooling with the Lifepac 8th Grade 5-Subject Set! This colorful set contains five core subjects: Bible, History and Geography, Science, Language Arts, and Math. Each individual subject in this Alpha Omega curriculum has ten worktexts and a teacher's guide. ...
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Mathematics
Our Mathematics Department at Red Bank Regional High School provides students with a challenging,
comprehensive course of study in mathematics. Freshmen are either placed in Algebra 1 or Geometry.
Algebra 1 provides a challenging curriculum, establishing a firm foundation in the Algebra needed for
success in subsequent courses. We also focus on helping students achieve success on the Algebra 1
End-of-Course exam, a NJ graduation requirement (starting with students enrolled in an Algebra 1
course in the 2010-2011 school year). Freshman placement will be determined by their previous math
experiences, ASK 8 scores, and our placement tests. Incoming freshmen who have taken Algebra 1 in
eighth grade will also take our placement tests and will need to submit the results of their Algebra
End-of-Course exam to determine their placement in Algebra 1 or Geometry. In addition, any student
who scores below 210 on the ASK 8 test or proves to be having difficulty in his/her current math course
will be assigned to a mathematics focused Study Hall. This Study Hall will reinforce the concepts discussed
in his/her current math course to ensure proficiency in math on the High School Proficiency Assessment and/or
the Algebra 1 End-of-Course exam. After successful completion of an Algebra 1 course, students will take
Geometry and Algebra 2 or Honors Algebra 2, building on their understanding of the relationship between
algebraic and geometric concepts through both abstract and real-world applications. Students will continue
to develop their inductive and deductive reasoning, communication skills, and problem-solving techniques.
A select group of students also have the option of taking Algebra 2 and Geometry in the same year, based on
their prior mathematics coursework. This allows them to take a second year of calculus or an alternate advanced
math elective in their senior year. The majority of our students will then take Pre-Calculus, which provides
essential concepts and skills of algebra, trigonometry, and the study of functions necessary for further study
in mathematics. For the motivated sophomores, juniors, and seniors, Honors Pre-Calculus, 3 levels of IB Math,
and AP Calculus are also offered. Some students, especially those interested in the Social Sciences, may elect
to take our Statistics/Discrete Mathematics course. Applied Math is offered to those students who have completed
Algebra 2 and are looking for success in taking college math placement tests as well as the SAT's. Any senior
needing to pass the HSPA is required to take HSPA Math, which is designed to develop the necessary mathematical
and problem solving skills in order to pass the HSPA, a graduation requirement. It is our hope that the
mathematics program will prepare the students at Red Bank Regional High School with the conceptual framework,
practical application and analytical skills necessary to meet the needs of application to real-world problems,
occupational uses, and their future study of mathematics.
Placement Factors
An incoming ninth grader's placement in Math is based on a combination of:
| 677.169 | 1 |
MECH 309 Numerical Methods in Mechanical Engineering (3 credits)
Overview
Mechanical Engineering : Numerical techniques for problems commonly encountered in Mechanical Engineering are presented. Chebyshev interpolation, quadrature, roots of equations in one or more variables, matrices, curve fitting, splines and ordinary differential equations. The emphasis is on the analysis and understanding of the problem rather than the details of the actual numerical program.
Terms: Winter 2013
Instructors: Mathias Legrand (Winter)
(3-1-5)
Prerequisites: MATH 263, MATH 271, COMP 208.
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This course may be used as a required or complementary course in the following programs:
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Rex, GA ACT MathYou will learn how to draw graphs of straight lines and parabolas. You will learn about the shapes of graphs for many types of equations. Algebra 1 also includes some statistics and probability and a small amount of geometry
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San Quentin Algebra 2 concepts build on each other so that future topics depend on understanding previous material. Therefore, misunderstanding one topic can cause continuous problems down the road. If this is left unaddressed, knowledge gaps compound over time and the student gets further behind've worked extensively in basic algebra and geometry, the foundations of advanced math study. My
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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0395746213
9780395746219
Introductory Algebra with Basic Mathematics:Introductory Algebra with Basic Mathematics is designed to be taught in all classroom settings, from lecture or small group classes to self-paced learning laboratories. The authors' acclaimed three-step interactive method lets students see a worked example, attempt a similar end-of-section exercise, and then see the complete solution to that exercise. Exercises concentrate on writing and research development, problem solving using real data, and exploring different strategies to solve problems.
| 677.169 | 1 |
Motivates and challenges more able students by providing more complex introductions, worked examples and exercises for all topics.
This specification is ideal for students to prepare for A level mathematics. A range of algebraic and geometric topics are covered and it provides an introduction to Matrices and Calculus.
Written by experienced teachers, this book:
- Offers complete support for students throughout the course as it is an exact match to this new specification
- Includes an introduction to each topic followed by worked examples with commentaries
- Provides plenty of practice with hundreds of questions
Contents
Section 1: Algebra
1. Number and algebra I
2. Algebra II
3. Algebra III
4. Algebra IV
Section 2: Geometry
5. Co-ordinate geometry
6. Geometry I
7. Geometry II
Section 3: Calculus
8. Calculus
Section 4: Matrices 9. Matrices
Review:
Motivates and challenges more able students by providing more complex introductions, worked examples and exercises for all topics; comprehensive support for the new AQA Certificate in Further Mathematics AAW9781444181128 AA69781444181128
Book Description:2013. Paperback. Book Condition: New. This brand new copy of AQA Certificate in Further Mathematics by Roger Porkess44181128
Book Description:Hodder Education44181128
Book Description:2013. Paperback. Book Condition: New. 190mm x 244mm x 12mm. Paperback. Motivates and challenges more able students by providing more complex introductions, worked examples and exercises for all topics; comprehensive support for the new AQA Certificate in Further Mathe.Shipping may be from our UK, US or Australian warehouse depending on stock availability. 256 pages. 0.560. Bookseller Inventory # 9781444181128
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Introduction to the Laplace Transform -
Summary: The purpose of this book is to give an introduction to the Laplace transform on the undergraduate level. The material is drawn from notes for a course taught by the author at the Milwaukee School of Engineering. Based on classroom experience, an attempt has been made to (1) keep the proofs short, (2) introduce applications as soon as possible, (3) concentrate on problems that are difficult to handle by the older classical methods, and (4) emphasize periodic phenomena. To make it possible to offe...show morer the course early in the curriculum (after differential equations), no knowledge of complex variable theory is assumed. However, since a thorough study of Laplace. transforms requires at least the rudiments of this theory, Chapter 3 includes a brief sketch of complex variables, with many of the details presented in Appendix A. This plan permits an introduction of the complex inversion formula, followed by additional applications. The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7. If additional time is available (e.g., four quarter-hours or three semester-hours), the whole book can be covered easily.The author is indebted to the students at the Milwaukee School of Engineering for their many helpful comments and criticisms.
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EOE STATEMENTWe are an equal employment opportunity employer. All qualified applicants will receive consideration for employment without regard to race, color, religion, gender, national origin, disability status, protected veteran status or any other characteristic protected byCarnegie Learning, a leading publisher of core and supplemental mathematics programs, was founded by cognitive and computer scientists in conjunction with practicing math teachers, and provides innovative research-based math curricula for middle and high school
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Complex Functions Theory C-11
In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.
Topics as Elementary complex functions, calculus of residua and its application to e.g. integration are illustrated.
ABOUT THE AUTHOR
Leif Mejlbro
Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until his retirement in 2003. He has twice been on leave, first time one year at the Swedish Academy, Stockholm, and second time at the Copenhagen Telephone Company, now part of the Danish Telecommunication Company, in both places doing research.
At the Technical University of Denmark he has during more than three decades given lectures in such various mathematical subjects as Elementary Calculus, Complex Functions Theory, Functional Analysis, Laplace Transform, Special Functions, Probability Theory and Distribution Theory, as well as some courses where Calculus and various Engineering Sciences were merged into a bigger course, where the lecturers had to cooperate in spite of their different background. He has written textbooks to many of the above courses.
His research in Measure Theory and Complex Functions Theory is too advanced to be of interest for more than just a few specialist, so it is not mentioned here. It must, however, be admitted that the philosophy of Measure Theory has deeply in
uenced his thinking also in all the other mathematical topics mentioned above.
After he retired he has been working as a consultant for engineering companies { at the latest for the Femern Belt Consortium, setting up some models for chloride penetration into concrete and giving some easy solution procedures for these models which can be applied straightforward without being an expert in Mathematics. Also, he has written a series of books on some of the topics mentioned above for the publisher Ventus/Bookboon.
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...When discussing particular problems, I like to first hear how a student thinks the problem should be approached. I will ensure that the student is approaching the problem in the most efficient way and will present alternative methods when applicable. My number-one goal is to help the student le...
...A class to help all those taking the SAT to achieve their greatest potential and to feel confident of doing well on the math section. Seeing the world through the use of linear models helps shed light on the mysteries around us and enriches each student with greater understanding of mathematics....Microsoft Excel is a powerful spreadsheet program that is commonly used in a variety of professional (e.g. business, engineering, medical, and etc.) settings. Many people also use Excel at home, for a host of different tasks ranging from balancing checkbooks to maintaining address lists. Like many successful software programs, Excel gets updated a lot.
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Identify the relative value of decimals, and correctly add and subtract, multiply, and divide with 100% accuracy.
List commonly used units of measure in the metric system, distinguish official abbreviations, express and convert metric weights and volumes, and apply them to apothecary measurements with greater than 81% accuracy.
Use a general understanding of IV therapy, to differentiate and identify calibrations; calculate flow rates, volume and time rates; and explain functions and protocol of IV administration with at least 81% accuracy.
General Education Learning Values & Outcomes
Revised August 2008 and affects outlines for 2008 year 1 and later.
8. Mathematical Reasoning
Definition:
Understanding and applying concepts of mathematics and logical reasoning in a variety of contexts, both academic and non-academic.
Outcomes: Students will be able to . . .
8.2 Correctly apply logical reasoning and mathematical principles to solve problems.
Course Contents
Decimals, add and subtract, multiply, and divide.
Commonly used units of measure in the metric system, official abbreviations, metric weights and volumes, and apothecary measurements.
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Welcome to The Amazing 7-Day Super-Simple, Scripted Guide to Teaching or Learning Decimals. I have attempted to do just what the title says: make learning decimals super simple. I have also attempted to make it fun and even ear-catching. The reason for this is not that I am a frustrated stand-up comic, but because in my fourteen years of teaching theDevelops the statistical approach to inverse problems with an emphasis on modeling and computations. The book discusses the measurement noise modeling and Bayesian estimation, and uses Markov Chain Monte Carlo methods to explore the probability distributions. It is for researchers and advanced students in applied mathematics. more...
The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use more...
This volume stresses the strong links between mathematics, culture and creativity in architecture, contemporary art, geometry, computer graphics, literature, theatre and cinema. It is designed not only for mathematicians but for anyone interested in culture, with a special emphasis on the visual aspects. more...
Dirac operators are used in physics, differential geometry, and group-theoretic settings. Using Dirac operators as a unifying theme, this work demonstrates how some of the important results in representation theory fit together when viewed from this perspective. It presents the important ideas on Dirac operators and Dirac cohomology. more...
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CGP Study Guide explains everything students need to know for Key Stage Three Maths - all fully up-to-date for the new curriculum from September 2014 onwards. It's ideal for students working at a higher level (it covers what would have been called Levels 5-8 in the pre-2014 curriculum). Every topic is explained with clear, friendly notes and worked examples, and there's a range of practice questions to test the crucial skills. We've also included a digital Online Edition of the whole book to read on a PC, Mac or tablet - just use the unique code printed at the front of the book to access it. For extra practice, a matching KS3 Maths Workbook is also available (9781841460383).
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Somehow CGP manage to produce guides which contain all the hard facts kids need for their exams, but which present them in a friendly, digestible format accessible to both children and adults. This comprehensive guide includes sections on numbers, algebra, shapes and statistics, presented with the usual CGP humour and cartoons. It is useful both as a reference book (when are shapes congruent and similar? What are the 8 simple rules of geometry?) and as a work-your-way through-it revision guide. Conclusion: everything you need for revising (and learning) KS3 maths.
My son was having problems in maths due to lessons missed after illness. I had very little knowledge of modern secondary level maths so this book was perfect to help us both to tackle some tricky new topics.
my 13 year old daughter was falling behind in her maths so i approached her maths teacher who recommended this book. we bought it for her and 4 weeks later she scored a 7C and secured her place in the top maths set for year 8. well worth every penny. i highly recommend this book.
A really good book that is worth reading it helps with your maths and covers all the catagories studied through Key Stage Three. With funny jokes and pictures it really makes Maths come to life, a brilliant read!!!
CGP books are absolutely fantastic for learning KS3 maths; I thoroughly recommend them for your first choice of guidebooks. There are 4 chapters, `Numbers Mostly' `Algebra' `Shapes' & `Statistics and Probability'. These are split into sections which explain all of the different parts - in amazing detail. CGP tell you everything you need to know and then test you at the end of the section; about 40 in-depth questions that will test your revision knowledge as far as it will go, and the answers are at the back of the book. You will find this book covers most topics, so this is a great buy.
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for a one-semester or two-quarter calculus course covering multivariable calculus for mathematics, engineering, and science majors.
Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher's voice beyond the classroom. That voice—evident in the narrative, the figures, and the questions interspersed in the narrative—is a master teacher leading students to deeper levels of understanding. The authors appeal to students' geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope.
The Instructor's Resource Guide and Test Bank provides a wealth of instructional resources including Guided Projects, Lecture Support Notes with Key Concepts, Quick Quizzes for each section in the text, Chapter Reviews, Chapter Test Banks, Tips and Help for Interactive Figures, and Student Study Cards.
Interactive Figures included in the ebook enable you and your students to manipulate the figures to bring to life hard-to-convey concepts.
Table of Contents
Chapter 8: Sequences and Infinite Series
8.1 An Overview
8.2 Sequences
8.3 Infinite Series
8.4 The Divergence and Integral Tests
8.5 The Ratio and Comparison Tests
8.6 Alternating Series
Chapter 9: Power Series
9.1 Approximating Functions with Polynomials
9.2 Power Series
9.3 Taylor Series
9.4 Working with Taylor Series
Chapter 10: Parametric and Polar Curves
10.1 Parametric Equations
10.2 Polar Coordinates
10.3 Calculus in Polar Coordinates
10.4 Conic Sections
Chapter 11: Vectors and Vector-Valued Functions
11.1 Vectors in the Plane
11.2 Vectors in Three Dimensions
11.3 Dot Products
11.4 Cross Products
11.5 Lines and Curves in Space
11.6 Calculus of Vector-Valued Functions
11.7 Motion in Space
11.8 Length of Curves
11.9 Curvature and Normal Vectors
Chapter 12: Functions of Several Variables
12.1 Planes and Surfaces
12.2 Graphs and Level Curves
12.3 Limits and Continuity
12.4 Partial Derivatives
12.5 The Chain Rule
12.6 Directional Derivatives and the Gradient
12.7 Tangent Planes and Linear Approximation
12.8 Maximum/Minimum Problems
12.9 Lagrange Multipliers
Chapter 13: Multiple Integration
13.1 Double Integrals over Rectangular Regions
13.2 Double Integrals over General Regions
13.3 Double Integrals in Polar Coordinates
13.4 Triple Integrals
13.5 Triple Integrals in Cylindrical and Spherical Coordinates
13.6 Integrals for Mass Calculations
13.7 Change of Variables in Multiple Integrals
Chapter 14: Vector Calculus
14.1 Vector Fields
14.2 Line Integrals
14.3 Conservative Vector Fields
14.4 Green's Theorem
14.5 Divergence and Curl
14.6 Surface Integrals
14.7 Stokes' Theorem
14.8 Divergence Theorem
About the Author(s)
William Briggs has been on the mathematics faculty at the University of Colorado at Denver for twenty-three years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, Using and Understanding Mathematics; an undergraduate problem solving book, Ants, Bikes, and Clocks; and two tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform. He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President's Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.
Lyle Cochran is a professor of mathematics at Whitworth University in Spokane, Washington. He holds BS degrees in mathematics and mathematics education from Oregon State University and a MS and PhD in mathematics from Washington State University. He has taught a wide variety of undergraduate mathematics courses at Washington State University, Fresno Pacific University, and, since 1995, at Whitworth University. His expertise is in mathematical analysis, and he has a special interest in the integration of technology and mathematics education. He has written technology materials for leading calculus and linear algebra textbooks including the Instructor's Mathematica Manual for Linear Algebra and Its Applications by David C. Lay and the Mathematica Technology Resource Manual for Thomas' Calculus. He is a member of the MAA and a former chair of the Department of Mathematics and Computer Science at Whitworth UniversitySeries
Packages
Pearson offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students, browse our available packages below, or contact your Pearson representative to create your own package Publications
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Applied Combinatorics
This book is designed for use by students with a wide range of ability and maturity. The stronger the students, the harder the exercises that can be ...Show synopsisThis book is designed for use by students with a wide range of ability and maturity. The stronger the students, the harder the exercises that can be assigned. The book can be used for one--quarter, two--quarter, or one--semester course depending on how much material is used. Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This book teaches students in the mathematical sciences how to reason and model combinatorically. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problem solving. The three principle aspects of combinatorical reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem (e.g. finding manageable subpieces or first solving the problem with three objects instead of n), and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.Hide synopsis
Description:Hardcover. New Condition. SKU: 9780470458389-1-0-3 Orders ship...Hardcover. New Condition. SKU: 9780470458389-1-0-3 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions. ISBN: 9780470458389
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What is missing in most curricula - from elementary school all the way through to university education - is coursework focused on the development of problem-solving skills. Most students never learn how to think...
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Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements...
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An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines that...
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"…a very useful resource for courses in nonparametric statistics in which the emphasis is on applications rather than on theory. It also deserves a place in libraries of all institutions where introductory...
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This landmark dissertation (1961) provides a systematic introduction to systems of modal logic and stands as the first presentation of what have become central ideas in philosophy of language and metaphysics,...
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On July 17, 2012, the centenary of Henri Poincaré's death was commemorated; his name being associated with so many fields of knowledge that he was considered as the Last Universalist. In Pure and Applied Mathematics,...
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An Introduction to the Statistical Theory of Classical Simple Dense Fluids covers certain aspects of the study of dense fluids, based on the analysis of the correlation effects between representative small groupings...
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The book Making Mathematics Practical (published by World Scientific in 2011) proposes a new paradigm in teaching problem solving in secondary school mathematics classrooms. It is a report of the research project...
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Differential Manifold is the framework of particle physics and astrophysics nowadays. It is important for all research physicists to be well accustomed to it and even experimental physicists should be able to...
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Paradoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano's Paradoxien. This volume contains an adept translation...
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This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie's opening...
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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians...
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Basic Math and Pre-Algebra Workbook For Dummies, 2nd Edition helps take the guesswork out of solving math equations and will have you unraveling the mystery of FOIL in no time. Whether you need to brush up on...
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Connecting Concepts to Problem-solving Documents
Main Document
Traditional quantitative problems of the type commonly found at the end of chapters in physics textbooks are assigned to students most introductory physics courses. Many students use a formula-driven approach to solve these problems that does not rely on understanding underlying physics concepts and that does little to encourage the problem-solving skills employed by experts. In another paper presented at this conference, we gave an example from electric circuits to illustrate the use of "bridging exercises" as part of students' homework to encourage students to solve problems by starting with developed physics concepts and models.1 In this paper, we describe our attempts to use the same approach in the context of electrostatics.
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Find a Mattapan Science
...Pre-calculus is the gate-keeper course for transition to calculus, and is therefore as important as calculus itself for those intending or needing to study higher mathematics. Typically it includes a review of basic algebra topics; various types of functions--including trigonometric and polynomi...
| 677.169 | 1 |
Cliffs Quick Review for Geometry - 01 edition
Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade.
At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less
Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies2001Wonder Book Frederick, MD
Cliffs Notes, 05/15/2001, Paperback, Good condition.
$1.99 +$3.99 s/h
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ISBN: 0201308150 / ISBN-13: 9780201308150
Mathematics All Around
* Problem-solving principles and strategies are introduced in chapter one and are used consistently throughout the text. * Of Further Interest ...Show synopsis* Problem-solving principles and strategies are introduced in chapter one and are used consistently throughout the text. * Of Further Interest sections appear at the end the chapter, and cover current topics that are exciting for students but are not typically part of the standard curriculum. * Statement Headings provide the students with a clear idea of the concept being discussed and are useful when reviewing for exams. * Applications motivate the discussion of the mathematics and increase student interest in the material. * Quiz Yourself questions are found throughout each section, and allow students to gauge their level of understanding before moving on to the next concept. * Some Good Advice is a feature that provides students with timely hints, tips, cautions and warnings about the material being covered. * Highlights are boxed features that consist of historical notes or biographical vignettes, uses of technology, and interesting applications.Hide synopsis
Sound copy, mild reading wear. May have scuffs or missing...Good. Sound copy, mild reading wear. May have scuffs or missing DJ. May have some note, highlighting or underlining. Purchasing this item helps us provide vocational opportunities to people with barriers to employmentReviews of Mathematics All Around
I cannot believe that all of this was crammed into ONE 8 week college course. I'm still getting over the stress of trying to make it through this course. The book is ok if you understand math, but if you don't, you're just going to be more lost than you were before you started. Very confusing
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Mathematics - Algebra (529 results)
The purpose of this book, as implied in the introduction, is as follows: to obtain a vital, modern scholarly course in introductory mathematics that may serve to give such careful training in quantitative thinking and expression as well-informed citizens of a democracy should possess. It is, of course, not asserted that this ideal has been attained. Our achievements are not the measure of our desires to improve the situation. There is still a very large "safety factor of dead wood" in this text. The material purposes to present such simple and significant principles of algebra, geometry, trigonometry, practical drawing, and statistics, along with a few elementary notions of other mathematical subjects, the whole involving numerous and rigorous applications of arithmetic, as the average man (more accurately the modal man) is likely to remember and to use. There is here an attempt to teach pupils things worth knowing and to discipline them rigorously in things worth doing.<br><br>The argument for a thorough reorganization need not be stated here in great detail. But it will be helpful to enumerate some of the major errors of secondary-mathematics instruction in current practice and to indicate briefly how this work attempts to improve the situation. The following serve to illustrate its purpose and program:<br><br>1. The conventional first-year algebra course is characterized by excessive formalism; and there is much drill work largely on nonessentials.
Florian Cajori's A History of Mathematics is a seminal work in American mathematics. The book is a summary of the study of mathematics from antiquity through World War I, exploring the evolution of advanced mathematics. As the first history of mathematics published in the United States, it has an important place in the libraries of scholars and universities. A History of Mathematics is a history of mathematics, mathematicians, equations and theories; it is not a textbook, and the early chapters do not demand a thorough understanding of mathematical concepts. The book starts with the use of mathematics in antiquity, including contributions by the Babylonians, Egyptians, Greeks and Romans. The sections on the Greek schools of thought are very readable for anyone who wants to know more about Greek arithmetic and geometry. Cajori explains the advances by Indians and Arabs during the Middle Ages, explaining how those regions were the custodians of mathematics while Europe was in the intellectual dark ages. Many interesting mathematicians and their discoveries and theories are discussed, with the text becoming more technical as it moves through Modern Europe, which encompasses discussion of the Renaissance, Descartes, Newton, Euler, LaGrange and Laplace. The final section of the book covers developments in the late 19th and early 20th Centuries. Cajori describes the state of synthetic geometry, analytic geometry, algebra, analytics and applied mathematics. Readers who are not mathematicians can learn much from this book, but the advanced chapters may be easier to understand if one has background in the subject matter. Readers will want to have A History of Mathematics on their bookshelves.
The Directly-Useful Technical Series requires a few words by of introduction. Technical books of the past have arranged themselves largely under two sections: the Theoretical and the Practical and the exercises are to be of a directly-useful character, but must at the same time be wedded to that proper amount of scientific explanation which alone will satisfy the inquiring mind. We shall thus appeal to all technical people throughout the land, either students or those in actual practice.
The present work is intended as a sequel to our Elementary Algebra for Schools. The first few chapters are devoted to a fuller discussion of Ratio, Proportion, Variation, and the Progressions, which in the former work were treated in an elementary manner; and we have here introduced theorems and examples which are unsuitable for a first course of reading.<br><br>From this point the work covers ground for the most part new to the student, and enters upon subjects of special importance: these we have endeavoured to treat minutely and thoroughly, discussing both bookwork and examples with that fulness which we have always found necessary in our experience as teachers.<br><br>It has been our aim to discuss all the essential parts as completely as possible within the limits of a single volume, but in a few of the later chapters it has been impossible to find room for more than an introductory sketch; in all such cases our object has been to map out a suitable first course of reading, referring the student to special treatises for fuller information.<br><br>In the chapter on Permutations and Combinations we are much indebted to the Rev. W. A. Whitworth for permission to make use of some of the proofs given in his Choice and Chance.
The present work contains a full and complete treatment of the topics usually included in an Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college.<br><br>Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinary processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers.<br><br>The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value.
The Directly Useful Technical Series requires a few words by way of introduction. Technical books of the past have arranged themselves largely under two sections: the theoretical and the practical, and the exercises are to be of a directly useful character, but must at the same time be wedded to that proper amount of scientific explanation which alone will satisfy the inquiring mind. We shall thus appeal to all technical people throughout the land, either students or those in actual practice.
Teacher's Manual for First-Year Mathematics is a book written by George William Myers, a Professor of the Teaching of Mathematics and Astronomy at the University of Chicago. The book is intended as a teaching manual for teachers instructing their students using a textbook called First Year Mathematics. Myers' book is intended as a companion piece to the textbook First Year Mathematics, released by the same publishing company, The University of Chicago Press. The book makes effort to assist the teacher by providing them with a detailed how-to regarding teaching the specific problems presented in the textbook. Teacher's Manual is presented in chapters, each corresponding to a chapter in First Year Mathematics. Specific references are made to page numbers and problems presented in the textbook. In total, the book contains fourteen different chapters. Teacher's Manual for First-Tear Mathematics can only be used in conjunction with the appropriate textbook. Without access to First Year Mathematics, the book is of no use. It is however an excellent companion piece to the textbook, and those able to access the original textbook will surely find this text to be highly beneficial. While a well-written teacher's manual, George William Myers' book assumes the reader has access to the original textbook. If you are interested in making use of this manual, do ensure that you are also able to access First Year Mathematics.
The orientalists who exploited Indian history and literature about a century ago were not always perfect in their methods of investigation and consequently promulgated many errors. Gradually, however, sounder methods have obtained and we are now able to see the facts in more correct perspective. In particular the early chronology has been largely revised and the revision in some instances has important bearings on the history of mathematics and allied subjects. According to orthodox Hindu tradition the Surya Siddhanta, the most important Indian astronomical work, was composed over two million years ago! Bailly, towards the end of the eighteenth century, considered that Indian astronomy had been founded on accurate observations made thousands of years before the Christian era. Laplace, basing his arguments on figures given by Bailly considered that some 3,000 years B. C. the Indian astronomers had recorded actual observations of the planets correct to one second; Playfair eloquently supported Bailly's views; Sir William Jones argued that correct observations must have been made at least as early as 1181 B. C.; and so on; but with the researches of Colebrooke, Whitney, Weber, Thibaut, and others more correct views were introduced and it was proved that the records used by Bailly were quite modern and that the actual period of the composition of the original Surya Siddhanta was not earliar than A. D. 400.<br><br>It may, indeed, be generally stated that the tendency of the early orientalists was towards antedating and this tendency is exhibited in discussions connected with two notable works, the Sulvasutras and the Bakhshali arithmetic, the dates of which are not even yet definitely fixed.
Rays Mathematical Series. Embracing a Thorough, Progressive, and Complete Course in Arithmetic, Algebra, and the Higher Mathematics. The Publishers will furnish any publications of the Eclectic Educational Series, sent by freight or express, on receipt of the wholesale price; or by mail for cost of mailing added. FJay sSeries: Rays New Primary Arithmetic Rays New Intellectual Arithmetic Rays New Elementary Arithmetic Rays New Practical Arithmetic Key to New Intellectual and Practical Arithmetics Rays New Higher Arithmetic Key to New Higher Arithmetic Rays New Test Examples in Arithmetic Rays Arithmetical Tablets (single, ioc.) per doz. Rays New Elementary Algebra Rays New Higher Algebra Key to Rays New Algebras Rays Test Problems in Algebra Rays Plane and Solid Geometry by Tappan). Rays Geometry and Trigonometry (by Tappan). Rays Analytic Geometry (by Howison) Rays New Astronomy (by Peabody) Rays Surveying and Navigation (by Schuyler). Rays Calculus (by Clark) Entered according to Act of Congress, in the year 1866, by Sargent, Wilson Hinkle, in the Clerks Office of the District Court of the United States for the Southern District of Ohio.
Bertrand Russell was a British logician, nobleman, historian, social critic, philosopher, and mathematician. Known as one of the founders of analytic philosophy, Russell was considered the premier logician of the 20th century and widely admired and respected for his academic work. In his lifetime, Russell published dozens of books in wildly varying fields: philosophy, politics, logic, science, religion, and psychology, among which The Principles of Mathematics was one of the first published and remains one of the more widely known. Although remembered most prominently as a philosopher, he identified as a mathematician and a logician at heart, admitting in his own biography that his love of mathematics as a child kept him going through some of his darkest moments and gave him the will to live. With his book The Principles of Mathematics, Russell aims to instill the same deep seated passion for mathematics and logic that he has carefully cultivated in the reader. He adeptly explores mathematical problems in a logical context, and attempts to prove that the study of mathematics holds critical importance to philosophy and philosophers. Russell utilizes the text to explore the some of the most fundamental concepts of mathematics, and expounds on how these building blocks can easily be applied to philosophy. In the second part of the book, Bertrand addresses mathematicians directly, discussing arithmetic and geometry principles through the lens of logic, offering yet another unique and groundbreaking interpretation of a field long before considered static. This book affords new insight and application for many basic mathematical concepts, both in roots of and application to other fields of scholarly pursuit. Russell uses his book to establish a baseline of mathematical understanding and then expands upon that baseline to establish larger and more complex ideas about the world of mathematics and its connections to other fields of personal interest. The Principles of Mathematics is a very captivating glimpse into the logic and rational of one of history's greatest thinkers. Whether you're a mathematician at heart, a logician, or someone interested in the life and thoughts of Bertrand Russell, this book is for you. With an incredible amount of information on mathematics, philosophy, and logic, this text inspires the reader to learn more and discover the ways in which these very disparate fields can interconnect and create new possibilities at their intersections.
Bringing to life the joys and difficulties of mathematics this book is a must read for anyone with a love of puzzles, a head for figures or who is considering further study of mathematics. On the Study and Difficulties of Mathematics is a book written by accomplished mathematician Augustus De Morgan. Now republished by Forgotten Books, De Morgan discusses many different branches of the subject in some detail. He doesn't shy away from complexity but is always entertaining. One purpose of De Morgan's book is to serve as a guide for students of mathematics in selecting the most appropriate course of study as well as to identify the most challenging mental concepts a devoted learner will face. "No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed," states De Morgan in his introduction. The book is divided into chapters, each of which is devoted to a different mathematical concept. From the elementary rules of arithmetic, to the study of algebra, to geometrical reasoning, De Morgan touches on all of the concepts a math learner must master in order to find success in the field. While a brilliant mathematician in his own right, De Morgan's greatest skill may have been as a teacher. On the Study and Difficulties of Mathematics is a well written treatise that is concise in its explanations but broad in its scope while remaining interesting even for the layman. On the Study and Difficulties of Mathematics is an exceptional book. Serious students of mathematics would be wise to read De Morgan's work and will certainly be better mathematicians for it.
This text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics which the engineer must emphasize, such as numerical computations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid.<br><br>The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject.<br><br>The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytic geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of effort.<br><br>The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest.
There are many men and women who, from lack of opportunity or some other reason, have grown up in ignorance of the elementary laws of science. They feel themselves continually handicapped by this ignorance. Their critical faculty is eager to submit, alike old established beliefs and revolutionary doctrines, to the test of science. But they lack the necessary knowledge.<br><br>Equally serious is the fact that another generation is at this moment growing up to a similar ignorance. The child, between the ages of six and twelve, lives in a wonderland of discovery; he is for ever asking questions, seeking explanations of natural phenomena. It is because many parents have resorted to sentimental evasion in their replies to these questionings, and because children are often allowed either to blunder on natural truths for themselves or to remain unenlightened, that there exists the body of men and women already described. On all sides intelligent people are demanding something more concrete than theory; on all sides they are turning to science for proof and guidance.<br><br>To meet this double need - the need of the man who would teach himself the elements of science, and the need of the child who shows himself every day eager to have them taught him - is the aim of the "Thresholds of Science" series.<br><br>This series consists of short, simply written monographs by competent authorities, dealing with every branch of science - mathematics, zoology, chemistry and the like. They are well illustrated, and issued at the cheapest possible price.
The Principles of Mathematics: Vol. 1 is a terrific introduction to the fundamental concepts of mathematics. Although the book's title involves mathematics, it is not a textbook packed with equations and theorems. Instead philosopher Bertrand Russell uses mathematics to explore the structure of logic. Russell's ultimate point is that mathematics is logic and logic itself is truth. The book is substantial and covers all subjects of mathematics. It is divided into seven sections: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. Russell covers all the major developments of mathematics and the contributions of important figures to the field. His sharp mind is evident throughout The Principles of Mathematics, as he challenges established rules and teachers readers how to think through difficult problems using logic. Russell was one of the great minds of the 20th Century. In this book he discusses how his ideas were influenced by the logician Peano. He also debates other philosophers and mathematicians, and even anticipates the Theory of Relativity, which had not yet been published by Einstein. One does not need to love mathematics to gain insights from The Principles of Mathematics: Vol. 1. Those who are interested in logic, intellectualism, philosophy or history will find significant insights into logical principles. Readers who desire an intellectual challenge will truly enjoy The Principles of Mathematics: Vol. 1.
Algebra is justly regarded one of the most interesting and useful branches of education, and an acquaintatice with it is now sought by all who advance beyond the more common elements. To those who would know Mathematics, a knowledge not merely of its elementary principles, but also of its higher parts, is essential; while no one can lay claim to that discipline of mind which education confers, who is not familiar with the logic of Algebra. It is both a demonstrative and a practical science a system of truths and reasoning, from which is derived a collection of Ilulee that maj be used in the solution of an endless variety of problems, not only interesting to the student, but many of which are of the highest possible utility in the arts of life. The object of the present treatise is to present an outline of this science in a brief, clear, and practical form. The aim throughout has been to demonstrate every principle, and to furnish the student the means of understanding clearly the rationale of every process he is required to perform. Io eflfort has been made to simplify subjects by omitting that which is difficult, but rather to present them in such a light as to render their acquisition within the reach of all who will take the pains to study. To fix the principles in the mind of the student, and to show their bearing and utility, great attention has been paid to the preparation of practical exercises. These are intended rather to illustrate the principles of the science, than as difficult problems to torture the ingenuity of the learner, or amuse the already skillful Algebraist. An effort has been made throughout the work to observe a.
E.R.Smith, E. Stephens, E. B. Stouffer, Eula A. Weeks, W. D. A. Westfall, Jessica M. Young.<br><br>On Friday evening at the American Hotel Annex a dinner was held jointly with the Southwestern Section of the American Mathematical Society and the Central Association of Science and Mathematics Teachers. Father W.J. Ryan, vice-president of St. Louis University and a member of the Association, acted as toastmaster at the dinner, and the following addresses were given: "The age of power" by Mr. A.S. Langsdorf, formerly dean of the Schools of Engineering and Architecture of Washington University; "Zoology in the secondary schools" by Dr. Caswell Grave, professor of zoology, Washington University.<br><br>At noon on Saturday the members of the Missouri Section of the Association and the Southwestern Section of the Society were the guests of Washington University at a luncheon which was served in the Tower Dormitory dining hall.<br><br>The following officers were elected for the ensuing year: Chairman, E. R. Hedrick, University of Missouri; Vice-Chairman, W.A. Luby, Kansas City Junior College; Secretary-Treasurer, P. R. Rider, Washington University.<br><br>The 1922 meeting will be held in Kansas City in November, at the time of the meeting of the Missouri State Teachers' Association.<br><br>The following papers were read:<br><br>(1) "Mathematics clubs in junior high schools" by Mr. A. H. Huntington, Cleveland High School, St. Louis;<br><br>(2) "Some suggestions in regard to mathematics" by Father W. J. Ryan, vice-president of St. Louis University;<br><br>(3) "Correct methods of making drawings of space objects" by Professor W. H. Roever, Washington University;<br><br>(4) "The relation of mathematics to engineering" by Professor E. R. Hedrick, University of Missouri;<br><br>(5) "Graphical methods of representing a function of a function and of solving allied problems" by Professors Hedrick and Roever;<br><br>(6)"An elementary exposition of the theorem of Bernoulli with applications to statistics" by Professor H.L. Rietz, University of Iowa;<br><br>(7) "Final report of the National Committee on Mathematical Requirements" by Dr. Eula A. Weeks, Cleveland High School, St. Louis.<br><br>In addition to these papers, an informal talk was given by Professor H. E. Slaught, of the University of Chicago, who told the Section of the recent grant to the Association by Mrs. Paul Carus of a sum of money to be used for the publication of expository monographs on mathematical subjects. In the absence of the author, the paper by Professor Rietz was read by Professor C. H. Ashton of the University of Kansas. Several of the papers led to interesting discussions. Abstracts of the papers follow below, the numbers corresponding to the numbers in the list of titles:<br><br>1. Mr. Huntington discussed mathematics clubs for pupils of junior high school age, maintaining that they offer opportunities not yet realized for enlisting the interest and effort of boys and girls in the study of mathematics.
The extended calculations required by some of the applications of trigonometry are laborious even to experienced computers, and to beginners are often a fruitful source of discouragement. Experience in making calculations and familiarity with the formulas employed suggest methods of arrangement by which skilful computers shorten their work and save much of their time. The aim should always be to secure the results to the required degree of accuracy with a minimum expenditure of time and labor. So far as the mechanical part of the work is concerned, the principal factors leading, to this end are the proper arrangement of the formulas employed the use of conveniently arranged tables having the needed helps for facilitating interpolation, and the use of no more places of decimals than are necessary to secure the desired accuracy in the results.<br><br>Orderly arrangement is almost indispensable to correct and rapid computation; on this account the practice of making computations on scraps of paper without systematic arrangement should not be followed. In the beginning, an outline of the entire solution should be made by writing the symbols of the quantities to be used in a vertical column, those to be combined being placed adjacent. In the same solution, turning more than once to the same place in the tables should be avoided, by taking at one opening all the functions of a given angle that may be required, and writing them in their proper places. The tables employed should be conveniently arranged, and, in general, should have auxiliary tables of proportional parts on the margins of the pages, so that the interpolations can easily be made mentally.<br><br>The number of decimal places to be used in any calculation is governed by the character of the data given, and the degree of accuracy required in the results. When the data have great precision, and the results are required with all attainable accuracy, seven decimal places must be used, or even a larger number.
This book has been planned to meet the needs of the first year mathematics in the ordinary high school, as well as to serve as a Third Course in Junior High School Mathematics.<br><br>Comparison with the traditional freshman course in ordinary high schools, will show that certain geometric matter of admitted value has been inserted, and some relatively useless topics have been omitted from the algebraic portions. This renders the book particularly suitable for use as a freshman text in mathematics in ordinary high schools, and it does not detract from its value as a Third Course in Junior High School Mathematics.<br><br>The review of arithmetic and of elementary geometric and algebraic notions, with which the book begins, is very desirable for any course of this type; and it makes the work usable either with or without the preceding books in the series.<br><br>The authors have been guided in their work by the following principles:<br><br>1. That there should be a high degree of continuity in the subject matter of mathematics and in the methods of presenting it during the three years of the Junior High School.
The facts of Algebra are of minor importance to the average individual and the subject should not be studied with the acquiring of these facts as the principal object to be attained. Algebra studied for the mere body of facts which it contains is a waste of time. These facts the student will of course acquire, but the authors believe they should come as incidentals to the acquiring of the methods and principles of the subject. The principal object, therefore, for both teacher and student to keep in mind is the acquisition, not of the facts, but of the underlying methods and principles, and we believe that when this is done the facts will be more intelligently comprehended and better retained.<br><br>We have endeavored to develop the topics treated in as logical and scientific a manner as was consistent with good pedagogy. The ground required for entrance to the scientific courses of the leading Colleges and Schools, or that required in the freshman year by the students in the course in arts has been covered, and in addition the needs of more advanced students have been kept in mind. Rather more ground is covered than is laid down in the requirements for the examinations in Advanced Algebra by the College Entrance Examination Board. In any case no difficulty will be experienced in omitting the extra parts if the teacher so desires.<br><br>The major portion of the book has been used in pamphlet form for several years with good results by the freshmen at Syracuse University.
This text differs widely from that marked out by custom and tradition. It treats the various branches of mathematics more with reference to their unities and less as isolated entities (sciences). It seeks to give pupils usable knowledge of the principles underlying mathematics and ready control of them. These texts are not an experiment; they were thoroughly tried out in mimeograph form on hundreds of high school pupils before being put into book form. The scope of Books I and II does not vary greatly from that covered in algebras and geometries of the usual type. However, Book I is different in that arithmetic, algebra, and geometry are treated side by side. The effect of this arrangement is increased interest and power of analysis on the part of the learner, and greater accuracy in results. Some pupils like arithmetic, others like algebra, still others like geometry; the change is helpful in keeping up interest. The study of geometry forces analysis at every step and stage; consequently written problems and problems to be stated have no terrors for those who are taught in this way. For several years mathematical associations have urged that all work should be based upon the equation. In accordance with this view we have made the demonstrations in this book largely algebraic, thus making the demonstration essentially a study in simultaneous equations. In this method of treatment, we have found it advantageous not to hurry the work. Pupils gain power, not in solving many problems, but in analyzing and tio?oxt 3 xaAwafcaxs.- ing the principles of a few.
The purpose o Fthis monograph is to present in a consecutive form the principal features of abstract and substitution group theory. The development of this branch of mathematics has been very rapid, especially in the last few years, and consequently there is much of great value to be found in a more or less fragmentary form throughout the various mathematical journals that has yet to be collected and discussed. It has been my purpose to examine in detail all memoirs dealing directly with such group theory (excluding, in particular, that of linear groups) and to construct from this material a continuous treatise on the subject. In order to secure uniformity of terminology and method I may seem to have taken liberties with the work of others, I trust that such will not be found unwarranted. The amount of space at my disposal has compelled me to omit all proofs; instead I have given with each theorem or definition a reference to nearly every source, original or secondary. Corrections or additions will be most gratefully appreciated. It is proper to add that as I was granted a Harrison Senior Fellowship to obtain opportunity for revising this work, its present form differs materially from that presented in May of 1901 to the Faculty of Philosophy of the University of Pennsylvania as a dissertation in partial fulfilment of the requirements for the degree of Doctor of Philosophy. The original draft was devoted to substitution theory alone and contained full proofs, with references to only the principal treatises.
Francis William Newman was an emeritus professor of University College in London and an honorary fellow of Worcester College, Oxford. Considered quite the renaissance man, Newman's interests ranged wildly, from writings on philosophy, English reforms, Arabic, diet, grammar, political economy, Austrian Politics, Roman History, and math. He wrote at length on every subject he found of interest, and this book, Mathematical Tracts is a testament to his very successful career as a mathematician and his eloquence as an impassioned author. At its core, this book explores many of the basics theorems and principles behind geometry, aimed at the budding mathematician to encourage interest and educate. A wonderful beginners guide, but also an interesting read for anyone wanting to refresh their foundational knowledge in geometry, this book is an easy to understand and approachable guide to mathematics. After establishing the basics, this book goes in-depth on many geometrical concepts such as the treatment of ration between quantities incommensurable and primary ideas of the sphere and circle. Newman's vast knowledge of mathematics is put to excellent use in this text, expounding on mathematical concepts and explaining them with such clarity that regardless of prior mathematical knowledge, the reader is guaranteed to understand the concepts. Newman highlights a variety of shapes such as pyramids and cones in their geometric context and explains their mathematical significance. He also expands the reader's understanding of parallel straight lines and the infinite area of a plane angle, and ends the book with a plethora of tables and helpful mathematical examples intended to further clarify the core concepts of the text. Truly a one of a kind, Mathematical Tracts is the perfect book for anyone interested in mathematics. Whether you're an early learner or a seasoned professional, you will find new information that is communicated in such a passionate and compelling way that it is impossible not to be enthused and excited about the topic. An incredibly approachable book laden with mathematical concepts that are made both interesting and exciting by the overwhelming passion of the author, this book is highly recommended for all readers.
April 5. 1919 Thit if one of an edition privately printed by the Rosemary Pm for the member of the Omar Khayyam Club of America. Limited to 200 copies, on American deckel-edged linen paper, bound with vellum back and antique paper ode. Copies numbered 1 to 100 reserved to Professor Story.100 copies numbered 1 Rto lOORreterved for the Rosemary Frew. This i No.
Sciences QLibranr 34 53 Preface The day has clearly passed when any comprehensive presentation of all dynamics could be compressed and unijfied within the compass of one moderate volume of homogeneous plan. The established connections of dynamical reasoning with other fields in physics are of increasing number and closeness, as furnishing for them strongly rooted sequences in their interpretative trains of thought and linking together what would else have continued to stand separate. And that relation has reacted powerfully in modern times upon dynamics itself, perpetually enriching its substance, yet at the same time introducing within it certain sharpening differences that are stamped upon it by the type of use for which preparation is being made. These in fact modify superficially the modes of expression and their tone, and shift their own emphasis through a range that brings about what is in effect a subdivision of territory and an acknowledgment of practically diverse interests. It is in response to the situation which has been thus unfolding, and in conformity with its drift toward manifold adaptations, that special treatises have been rendered available whose measure of unquestioned excellence and authority would make superfluous an attempt to replace any such unit with a marked improvement upon it. But undoubtedly these differentiations founded in divergencies and inevitably expressing them in some degree, are entailing a corresponding need and demand to offset them with a broadening survey of the common foundation and of the common stock of resources. And with that end in view another treatment of dynamics finds a place for itself and holds it for special service.
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Problems and Solutions in Mathematical Finance, Volume I: Stochastic Calculus Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an…
The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book
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Precalculus: Concepts Through Functions A Right Triangle - 2nd edition
Summary: Pre-calculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, Second Edition embodies Sullivan/Sullivan's hallmarks accuracy, precision, depth, strong student support, and abundant exercises while exposing readers to functions in the first chapter. To ensure that students master basic skills and develop the conceptual understanding they need for the course, this text focuses on the fundamentals: preparing for class, practicing their homework, a...show morend reviewing the concepts. After using this book, students will have a solid understanding of algebra and functions so that they are prepared for subsequent courses, such as finite mathematics, business mathematics, and engineering calculus. KEY TOPICS: Functions and Their Graphs; Linear and Quadratic Functions; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Trigonometric Functions; Analytic Trigonometry; Applications of Trigonometric Functions; Polar Coordinates; Vectors; Analytic Geometry; Systems of Equations and Inequalities; Sequences; Induction; the Binomial Theorem; Counting and Probability; A Preview of Calculus: The Limit; Derivative, and Integral of a Function MARKET: For all readers interested in pre-calculus28.01 +$3.99 s/h
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May contain some highlighting. Supplemental materials may not be included. We select best copy available. - 2nd Edition - Hardcover - ISBN 9780321645081
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Algebra for College Students
This text covers traditional material and integrates it into the whole spectrum of learning. It contains a vast collection of historical references, ...Show synopsisThis text covers traditional material and integrates it into the whole spectrum of learning. It contains a vast collection of historical references, interdisciplinary applications, enrichment essays, thought-provoking exercises, and word problems. algebra, and provides comprehensive coverage of the topics required in a strong one term course in Intermediate Algebra or in a one-term course entitled Algebra for College Students.Hide synopsis
Description:New. May not contain access codes or supplementary material....New. May not contain access codes or supplementary material. 2nd day shipping available, ships same or next business day. Get bombed! ! This is the U.S. student edition as pictured unless otherwise stated.
Description:Fair. Missing the front cover. May not contain access codes or...Fair. Missing the front cover. May not contain access codes or supplementary material. 2nd day shipping available, ships same or next business day. Get bombed! ! This is the U.S. student edition as pictured unless otherwise stated.
Description:Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780321758958927.
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GRE Subject Mathematics
The test consists of approximately 66 multiple-choice questions drawn from courses commonly offered at the undergraduate level.
Approximately 50 percent of the questions involve calculus and its applications — subject matter that can be assumed to be common to the backgrounds of almost all mathematics majors.
About 25 percent of the questions in the test are in elementary algebra, linear algebra, abstract algebra and number theory. The remaining questions deal with other areas of mathematics currently studied by undergraduates in many institutions.
The following content descriptions may assist students in preparing for the test. The percents given are estimates; actual percents will vary somewhat from one edition of the test to another.
CALCULUS — 50%
Material learned in the usual sequence of elementary calculus courses — differential and integral calculus of one and of several variables — includes calculus-based applications and connections with coordinate geometry, trigonometry, differential equations and other branches of mathematics.
ALGEBRA — 25%
Elementary algebra: basic algebraic techniques and manipulations acquired in high school and used throughout mathematics
Other topics: general topology, geometry, complex variables, probability and statistics, and numerical analysis
The above descriptions of topics covered in the test should not be considered exhaustive; it is necessary to understand many other related concepts. Prospective test takers should be aware that questions requiring no more than a good precalculus background may be quite challenging; such questions can be among the most difficult questions on the test. In general, the questions are intended not only to test recall of information but also to assess test takers' understanding of fundamental concepts and the ability to apply those concepts in various situations
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97804719709hematics in Engineering and Science
In today's world, technology plays an increasingly important role. At the same time, mathematics is finding ever wider areas of application as we seek to understand more about the way in which nature works. Traditionally, engineering and science have relied on mathematical models for design and for the prediction of the behaviour of phenomena. Although widespread availability of computers and pocket calculators has reduced the need for long, tedious calculations to be carried out manually, it is still important to be able to perform simple calculations in order to have a feel for the processes involved. This book starts with a detailed synopsis of the material included in the authors' related textbook Foundation Mathematics (Wiley, 1998). It then expands the material in the areas of trigonometry, solution of equations and algebra. Vectors are covered next, then calculus is taken forward into geometrical applications. Matrix algebra and uncertainty follow before deeper analysis in chapters on integer variables, differential equations and complex numbers leads towards an appendix on mathematical modelling. Each chapter opens with a list of learning objectives and ends with a summary of key points and results. A generous supply of worked examples incorporating motivational applications is designed to build knowledge and skill. Drill and practice is essential and the exercises are graded in difficulty for reading and revision: the answers at the end of each chapter include helpful hints. Use of a pocket calculator is encouraged where appropriate. Many of the exercises can be validated by computer algebra and its use is strongly recommended where higher algebraic accuracy can be achieved and drudgery removed. The concise and focused approach of Mathematics in Engineering and Science will enable the student reader to approach the challenges of mathematics in a course at university level with confidence.
Foundation Mathematics and Mathematics in Engineering and Science are written to be both complementary and independent; students may follow both books consecutively or may use just one, depending on their previous mathematical experience and the level of mathematical development that they wish to achieve
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Z Spot Teacher Kits EZ Spot Teacher Kits
The TI-34 MultiView scientific calculator was designed with educator input in mind for use in these middle grades math and science classes: Middle School Math, Pre-Algebra, Algebra I & II, Trigonometry, General Science, Geometry and Biology.
In Classic mode, the TI-34 MultiView can be used in the same classrooms as the TI-34 II Explorer Plus as the screen appears identical to the TI-34 II Explorer Plus in this mode.
MultiView Display View multiple calculations on a 4-line display and scroll through entries with ease. See math expressions and symbols, including stacked fractions, exactly as they appear in textbooks
Fraction Exploration The TI-34 MultiView scientific calculator comes with the same features that made the TI-34 II Explorer Plus so helpful at exploring fraction simplification, integer division and constant operators.
Data List Editor Enter statistical data for 1- and 2-var analysis as well as for exploring patterns via list conversions to see different number formats like decimal, fraction and percent side-by-side.
Scrolling & Editing Scroll through entries with ease. Students can investigate patterns similar to using a graphing calculator.
Learn more about the Texas Instruments TI-34 MultiView (34MV/TKT/1L1/
Specification
Type
Calculators & Accessories
General
Brand
Texas Instruments
Model
TI-34 MultiView (34MV/TKT/1L1/
Features
Features
The TI-34 MultiView scientific
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Find a NorcrossAlgebraic math is a major stepping stone to multiple sciences and must be mastered to facilitate future academic progress in the sciences. As algebra skills consolidate, we move toward calculus (differential and integration calculus) which employs extremely powerful math skills. Pre-calculus is the bed rock of algebraic math upon which calculus stands
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Tag Archives: MathematicsFinding the domain and range of functions confuses many students. Using color to code the domain and range separately helps students distinguish domain and range, and thereby helps them find the domain and range for continuous functions
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Abstract: Representation is discussed in the context of solving a system of linear equations. Five representations [concrete, tables, graphs, algebraic, matrices] are viewed from perspectives of understanding, technology, generalization, exact vs approximate solution, and learning style.
The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
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Florida's population growth. The results show that students often do not have a clear grasp of the differences between linear growth and exponential growth.
College Algebra or Liberal Arts math students are presented with three Questions of the Day and a write-pair-share activity...
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College Algebra or Liberal Arts math students are presented with three Questions of the Day and a write-pair-share activity involving Florida's population growth (other states may be used in place of Florida). The results are quite revealing and show that while students may have learned how to perform the necessary calculations, their conceptual understanding concerning exponential growth may remain faulty. Student knowledge (or lack thereof) of the size of their state's population and its annual growth rate may also be surprising.
College Algebra or Liberal Arts math students are presented with a ConcepTest and a write-pair-share activity involving...
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College Algebra or Liberal Arts math students are presented with a ConcepTest and a write-pair-share activity involving Florida's population growth. The activity asks students to decide whether a ten-year growth rate can be divided by 10 to produce the corresponding annual growth rate for each of the ten years. The results show that, while students may have learned that exponential growth is a multiplicative process, their conceptual understanding concerning exponential growth is often a bit fuzzy.
College Algebra or Liberal Arts math students are presented with a Question of the Day and a write-pair-share activity...
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College Algebra or Liberal Arts math students are presented with a Question of the Day and a write-pair-share activity involving U.S. state population growth. Student knowledge (or lack thereof) of the annual growth rates of individual states may be surprising.
'Students will identify a direct variation, solve linear equations, and create tables based on the exercise equipment...
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'Students will identify a direct variation, solve linear equations, and create tables based on the exercise equipment provided for astronauts on long duration missions on the International Space Station (ISS) in order to maintain their fitness to perform mission objectives and to return to Earth without serious health complications. Students willidentify direct variation from ordered pairs by calculating the constant of variation;calculate slope from two points using the slope formula;determine independent and dependent variables;solve linear equations; andcreate tables.'Links are provided here for both the teacher's information and the students' information.
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Problem Solving Approach to Mathematics for Elementary School Teachers, A (11th Edition)
9780321756664
ISBN:
0321756665
Edition: 11 Pub Date: 2012 Publisher: Addison Wesley
Summary: This is the leading textbook for students learning how to teach mathematics to elementary school students, focusing on problem solving. It remains current with its discussion of standards in teaching today and it teaches students the value of professional development for their future careers. It encourages active learning and provides many exercises, study tools and opportunities for active learning. Students will ga...in valuable insight into how they can apply their mathematics and teaching knowledge in the classroom. We offer many high quality discounted mathematics textbooks to buy or rent by semester.
Rick Billstein is the author of Problem Solving Approach to Mathematics for Elementary School Teachers, A (11th Edition), published 2012 under ISBN 9780321756664 and 0321756665. Four hundred ninety eight Problem Solving Approach to Mathematics for Elementary School Teachers, A (11th Edition) textbooks are available for sale on ValoreBooks.com, eighty seven used from the cheapest price of $69.09, or buy new starting at $173 with additional notes or answers. New Condition. SKU:... [more] [more loose-leaf edition textbook (same content, just cheaper!!). May not contain access codes or supplementary material. 2nd day shipping available, ships same [more]
ALTERNATE EDITION: This is a loose-leaf edition textbook (same content, just cheaper!!). ANNOTATED INSTRUCTOR'S EDITION contains the COMPLETE STUDENT TEXT with some instructor comments or answers. May not include student CD or access code. Has some shelf wear, hig [more]
ALTERNATE EDITION: ANNOTATED INSTRUCTOR'S EDITION contains the COMPLETE STUDENT TEXT with some instructor comments or answers. May not include student CD or access code. Has some shelf wear, highlighting, underlining and/or writing
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Education. Homework and Mentals Books revise and consolidate what they have learnt. It isn't an item that we generally keep in stock at Booktopia's Sydney Warehouse but it is one that we can source ve...
Nelson Maths 9 text bookisbn 9780170 123686 484pages long plus cd which wasn't used. Nelson Maths Facts 9 Level 6 is a small booklet of 40 pages. It also has been laminated and has a crossed out name ...
Jacaranda Maths Quest 11 Mathematical Methods CAS and. The companion book is in like new condition with no creases or markings inside. The textbook is in fair condition with normal signs of use includ...
Maths Plus 2 by Harry O'Brien ISBN: 9780195519587. Education. Homework and Mentals Books revise and consolidate what they have learnt. Shipping Delivery. Sign up to our newsletter to hear about about ...
Maths Plus 6 by Harry O'Brien ISBN: 9780195519228. Education. Homework and Mentals Books revise and consolidate what they have learnt. Shipping Delivery. Sign up to our newsletter to hear about about ...
Maths Quest 10 for the Australian Curriculum provides students with essential mathematical skills and knowledge through the content strands of Number and Algebra, Measurement and Geometry, and Statist...
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Essential Mathematics for Economic Analysis - 2nd edition
Summary: Essential Mathematics for Economic Analysis provides an invaluable introduction to mathematical analysis and linear algebra for economists. Its main purpose is to help students acquire the mathematical skills they need in order to read the less technical literature associated with economic problems. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics usually taught in undergraduate course...show mores on mathematics for economists. Features
Large number of examples throughout the book help to link abstract mathematics with real life
Extremely clear writing style without sacrificing mathematical precision and rigour ensures that students gain a thorough understanding of the use of mathematics to analyse economic problems.
Extensive number of problems and exercises at the end of each section with solutions to odd-numbered questions at the back of the book, allowing students to constantly practice what they are learning to reinforce their understanding.
New To This Edition
Most chapters have been revised and updated. They now include additional problem material and many more examples
Key concepts and techniques placed in colour and boxes to outline their importance
New chapter 17 on Linear Programming
Extensive resources for instructors and students on the companion website at including Instructors Manual with tests; Excel supplement with exercises; Excel supp Answers for lecturers; Downloadable Exam style problems which can be set as assignments for students27 +$3.99 s/h
Good
worldofbooks Goring-By-Sea,
2005 Trade paperback 2nd Revised ed. Good. The book has been read but remains in clean condition. All pages are intact and the cover is intact. Some minor wear to the spine. Trade paperback (US). Gl...show moreued binding. 714
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*This course is open to all WV educators who hold or have held mathematics certification or multi-subject K-8 certification.
Course Syllabus
Using Patterns to Develop Algebraic Thinking
Catalog Description
Prerequisites
Participants are expected to have regular access to computers. In addition, participants should be proficient with using email, browsing the Internet, and navigating to computer files.
Goals
This workshop will enable participants to:
Develop an understanding of mathematical and algebraic thinking
Recognize and build on opportunities for algebraic thinking in a variety of mathematics contexts
Analyze students' algebraic thinking
Pose questions that encourage the development of algebraic thinking
Assessment and Course Requirements
Each session includes readings, an activity and a discussion assignment, which participants are required to complete.
Course Products
As a final product, participants will create a lesson plan based on the strategies and concepts they have explored throughout the workshop.
Discussion Participation
Participants will be evaluated on the frequency and quality of their discussion board participation. Participants are required to post a minimum of two substantial postings each session, including one that begins a new thread and one that responds to an existing thread. Postings that begin new threads will be reviewed based on their relevance, demonstrated understanding of course concepts, examples cited, and overall quality. Postings that respond to other participants will be evaluated on relevance, degree to which they extend the discussion, and tone.
Required Readings, Activities and Assignments
Session One: What is Algebraic Thinking?
In this session's activity, participants will solve the "Crossing the River" algebra problem, paying attention to their mathematical strategies and taking notes about them.
Session Two: Examining Your Own Thinking through Algebraic Problems
Participants will explore the "Painting Faces" problem and reflect on their own thinking, as a starting point for examining student thinking in later sessions.
Session Three: Analyzing Students' Algebraic Thinking about Patterns
Participants will study two examples of student work and look for evidence of algebraic thinking in each. They will subsequently watch two videos in which the students explain their thinking processes as they worked on the problem.
Session Four: Using Teacher Questioning to Explore Algebraic Thinking
Participants will solve the "V-Patterns" problem independently, noting their own approach to the problem. They will then watch four video clips in which a classroom teacher poses questions about the "V-Patterns" problem to students, and consider which questions effectively elicit algebraic thinking from the students.
Session Five: Conducting a Student Interview
Participants will solve the "Tiling Garden Beds" problem, and then interview two students to learn about their thinking and their ability to generalize in their solution to the "Tiling Garden Beds" problem.
Participants will use the Algebraic Thinking Lesson Plan Template to design a lesson plan incorporating what they have learned about analyzing students' mathematical thinking and developing good questions.
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Tukwila, WA PhysicsIt allows one to perform numerical calculations much faster compared to programming languages like C, C++ and Java. We can visualize the results using graph plotting. I have been using Matlab software to solve mathematical problems such as Linear equations, non-linear equations, First order differential equations, second order differential equations.
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Mathematical Reasoning Writing And Proof
9780131877184
ISBN:
0131877186
Edition: 2 Pub Date: 2006 Publisher: Prentice Hall
Summary: Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs. Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with " Preview Activities" at the start of each section. Includes " Activities" throughout that relate to the material contained in each sectio...n. Focuses on Congruence Notation and Elementary Number Theorythroughout. For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
Sundstrom, Ted is the author of Mathematical Reasoning Writing And Proof, published 2006 under ISBN 9780131877184 and 0131877186. One hundred five Mathematical Reasoning Writing And Proof textbooks are available for sale on ValoreBooks.com, three used from the cheapest price of $12.34, or buy new starting at $28.95.[read more]
Ships From:Salem, ORShipping:Standard, ExpeditedComments:Has minor wear and/or markings. SKU:9780131877184-3-0-3 Orders ship the same or next business day... [more]
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Browse related Subjects
Supported by precise examples, this text provides thorough discussions of the maths topics needed for success in business. It features a comprehensive overview of business maths, and offers insightful background material in the fields of retailing, finance and accounting.Supported by precise examples, this text provides thorough discussions of the maths topics needed for success in business. It features a comprehensive overview of business maths, and offers insightful background material in the fields of retailing, finance and accounting321500121
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Texas Algebra I
Do you put the fun in functions, or is rational the last thing you feel when you encounter a rational expression? Was PEMDAS the name of your first dog, or is FOIL just something you wrap lovingly over last night's meatloaf? (You may think we've run out of math puns, but we're just getting warmed up.) Shmoop's guide to the Texas Algebra I End-of-Course Assessment gives you everything you'll need to navigate the variable-infested waters of functions, equations, and inequalities.
What's Inside Shmoop's Online Texas EOC Algebra I PrepHere, you'll find…
extreme topic review (for the extreme student)
practice drills to drill concepts into your brain
multiple full-length practice exams to get that full-length experience
test-taking tips and strategies from experts who know what they're talking about
step-by-step guides to taking down essay questions
chances to earn Shmoints and climb the leaderboard
A purchase gives you unlimited access for 12 months.
Sample Content
Properties and Attributes of Functions
We learned how to add a long time ago. And when we say long, we mean long—maybe as far back as first grade, even. We probably did a little adding, took a little test, and never had to deal with it again for the rest of our lives.
If only.
Addition might have become second nature to us, like walking or tying our shoes, but that doesn't mean that we've stopped using it. As we see time after time, math is cumulative. There are about 12 questions on the Texas Algebra I EOC exam that address these basics about functions. But we can't just think about these concepts on their own; we need to remember them when we move on to more specific topics. Like linear functions, for instance.
In this section, we'll talk about domain and range. Then we'll apply it later. We'll talk about interpreting graphs. Then we'll apply it later. Hopefully, you're starting to sense a pattern here
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this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces"-- Provided by publisher.
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